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AUTHOR: 


READ,  CARVETH 


Til  IE: 


LOGIC. 

AND  INDUCTIVE 


PLA  CE 


LONDON 


DATE 


1898 


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'•:"  Read,  Qarvetlu  1848- 


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Logic,  deauctive  and  inductive.     By  Carveth  Read,  ....     l^hrtd 
edition,- revised-and^nlarged.     London,  A.  Moring,  ltd.,  l^eS:  1898 

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LOGIC 

DEDUCTIVE   AND   INDUCTIVE 


LOGIC 

DEDUCTIVE  AND  INDUCTIVE 


(■ 


BY 


CARVETH    READ,    M.A. 


LONDON 
GRANT   RICHARDS 

9  HENRIETTA  STREET.  COVENT  GARDEN 

1898 


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Printed  by  Ballantyne,  Hanson  &>  Co. 
At  the  Ballantyne  Press 


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PREFACE 

SEPARATION  Of  the  facts  and  laws  of  Nature  into  departments 
for  the  convenience  of  study,  has  been  one  of  the  chie    con- 
ditions of  scientific  progress.     It  is  true  that  such  separation^ 
made  for  our  convenience  and  does  not  exist  in  Natu  e.     Yet 
it  has  been  the  means  of  revealing  the  ""'^V^f. Mature    he 
connection  of  facts,  the  harmony  of  laws:  analysis  ha    been 
the   necessary   preliminary   to   an    intelligent    synthesis      No 
further  apology  need  be  offered  for  the  separation  "f  Logic^^m 
the  present  volume,  from  all  other  studies,  and  especial^  tar. 
Psvchology  and  Metaphysics,  with  greater  rigour  than  has  been 
usual  in  logical  treatises  :  carrying  out  the  plan  that  elsewhere 
has  always  proved  advantageous. 

The  instructed  reader  will  easily  see  that  I  have  been  chiefly 
indebted  to  Mill's  SysUm  of  Logic,  Professor  Bains  Logtc^r 
Venn's  Smprual  Logic,  and  Dr.  Keynes'  For,naUog>c.  What- 
ever is  due  to  other  authors  has  been  acknowledged  as  occasion 
arose.  /In  every  case  I  have  tried  to  make  the  property  con- 
veyed my  own :  an  excuse  for  theft  that  must  seem  odd  to  a 
lawyer,  but  is  well  recognised  in  the  courts  of  literature.  > 

For  the  comprehensive  study  of  contemporary  opinion  on 
Logic,  several  books  besides  the  above-mentioned  are  needed : 
especially  Mr.  Bradley's  FrinciJ,/es  of  Logic,  Mr.  Alfred  S.dg- 
v^^ckl  Process  of  Argument,  and  Mr.  BosanqUet's  Logrc :  or  the 
Morphology  of  Knowledge.  The  last  author's  ^— / 
Lojc  is  expressly  intended  to  popularise  his  views.  M  .  Hob 
house's  Theory  of  Kno^.Mge,  an  original  and  valuable  treatise, 

263408 


QC 


VI 


PREFACE 


did  not  come  into  my  hands  until  this  book  was  finished  (now 
some  time  ago) :  else,  probably,  I  should  often  have  referred 
to  It.  Those  who,  not  reading  German,  desire  to  see  a  sample 
of  the  present  state  of  Logic  in  the  empire,  may  be  referred  to 
Professor  Sigwart's  Zoo^i^,  recently  translated.  Ueberweg's 
Sysfem  of  Logic,  atid  History  of  Logical  Doctrines  is  invaluable 
in  its  historical  passages. 

I  owe  a  great  deal  to  Mr.  Alfred  Sidgwick,  Mr.  Thomas 
Whittaker  and  Professor  C.  M.  Thompson,  who  have  been  at 
pams  to  advise  me  upon  portions  of  the  MS.  and  proofs. 
Most  of  the  chapters,  however,  no  one  but  myself  has  seen  ; 
so  that  whatever  errors  the  critic  may  find  must  occur  in  those 
unsponsored  chapters;  and  it  is,  therefore,  needless  to  say 
which  they  are. 


CARVETH  READ. 


London,  May  1898. 


CONTENTS 


Preface 


CHAPTER  I 


INTRODUCTORY 


lAGE 
V 


§  I.  Definition  of  Lx)gic 

§  2.  General  character  of  proof     . 

§  3.  Division  of  the  subject    . 

§  4.   Uses  of  Logic  .         .         .         • 

§  5.  Relation  of  Logic  to  other  sciences 

to  Mathematics  (p.  7) )  to  concrete  Sciences  (p.  8) ;  to 
Metaphysics  (p.  8) ;  to  regulative  sciences  (p.  10) 
§  6.  Schools  of  Logicians 

Relation  to  Psychology 


I' 

2 

3 

4- 
7 


10 
II' 


CHAPTER  II 

GENERAL    ANALYSIS    OF    PROPOSITIONS 


§  I.  Propositions  and  Sentences    . 

§  2.  Subject,  Predicate  and  Copula 

§  3.  Compound  Propositions 

§  4.  Import  of  Propositions   . 

§  5.  Form  and  Matter    . 

§  6.  Formal  and  Material  Logic     . 

§  7.  Symbols  used  in  Logic    . 


14 

}^ 

15 

16 

19- 

20  • 

21 


Vlll 


CONTENTS 


CONTENTS 


CHAPTER  III 


OF  TERMS  AND  THEIR  DENOTATION 


§  I .  Some  Account  of  Language  necessary    . 

§  2.  Logic,  Grammar  and  Rhetoric        .         .         .         . 

§  3.  Words  are  Categorematic  or  Syncategorematic 

§  4.  Terms  Concrete  or  Abstract 

§  5.  Concrete  Terms,  Singular,  General  or  Collective  . 


CHAPTER  IV 


THE    CONNOTATION    OF    TERMS 


§  I.  Connotation  of  General  Names 
§  2.  Question  of  Proper  Names 

other  Singular  Names 
§  3-  Question  of  Abstract  Terms   . 
§  4.  Univocal  and  Equivocal  Terms 

Connotation  determined  by  the  suppositio 
§  5.  Absolute  and  Relative  Terms 
§  6.  Relation  of  Denotation  to  Connotation  . 
§  7.  Contradictory  Terms       .... 
§  8.  Positive  and  Negative  Terms 

Infinites 

Privatives 

Contraries 


CHAPTER  V 


CLASSIFICATION    OF    PROPOSITIONS 


§  I.  As  to  Quantity 

Quantity  of  the  Predicate 
§  2.  As  to  Quality  .         .         .         . 

Infinite  Propositions 


PAGE 

24 

25 
26 
27 
29 


32 
33 

34 

35 

35 

37 

37 

39 
40 

43 

43 
43 
43 


45 

47 

48 

48 


§  3.  A.  I.  E.  O.       . 

§  4.  As  to  Relation 

Change  of  Relation  . 

§  5.  As  to  Modality 

§  6.  Verbal  and  Real  Propositions 


CHAPTER  VI 

CONDITIONS    OF    IMMEDIATE    INFERENCE 


8  I    Meaning  of  Inference 

§  2.  Immediate  and  Mediate  Inference 

§  3.  The  Laws  of  Thought     . 

84.  Identity  .        •         •         •         •         ' 
§  5    Contradiction  and  Excluded  Middle 
§  6.  The  Scope  of  Formal  Inference      . 


CHAPTER  VII 

IMMEDIATE    INFERENCES 

Plan  of  the  Chapter  .  •  •  • 
Subalternation  .  •  •  •  ' 
Connotative  Subalternation  . 

Conversion  .••••■ 
Obversion  .  •  •  •  "  " 
Contrary  Opposition  .  •  •  • 
Contradictory  Opposition      . 

§    8.  Subcontrary  Opposition 

§    9    The  Square  of  Opposition      . 

§  10.  Secondary  modes  of  Immediate  Inference 

§11.  Immediate  Inferences  from  Conditionals 


§ 


I. 

2. 

3- 

4 

5 
6. 

7- 


IX 

PAGE 

49 

50 
51 

54 
55 


57- 

58 
60- 

61 

62 

64 


,          •          •          * 

67 

67 

68 

69 

71 

72 

73 

74 

74 

, 

75 

77 

CONTENTS 


CHAPTER  VIII 

ORDER    OF    TERMS.     EULER's    DIAGRAMS.     LOGICAL    EQUATIONS. 
EXISTENTIAL    IMPORT    OF    PROPOSITIONS 

PAGE 

§  I.  Order  of  Terms  in  a  proposition 79 

§  2.  Euler's  Diagrams .80 

§3.  Propositions  considered  as  Equations 83 

§  4.  Existential  Import  of  Propositions 86 


CHAPTER  IX 

FORMAL    CONDITIONS    OF    MEDIATE    INFERENCE 

§  I.  Nature  of  Mediate  Inference  and  Syllogism    ....         89 

§  2.  General  Canons  of  the  Syllogism 90 

Definitions  of  Categorical  Syllogism ;  Middle  Term ; 
Minor  Term ;  Major  Term ;  Minor  and  Major  Pre- 
mise (p.  91) 
Illicit  Process  (p.  92)  ;  Distribution  of  the  Middle  (p.  92) ; 
Effects  of  Negative  Premises  (p.  93) ;  of  Particular 
Premises  (p.  94) 

§  3.  Dictum  de  omni  et  niillo 95 

§  4.  Syllogism  in  relation  to  the  Laws  of  Thought         ...         96 
§  5.  Other  Kinds  of  Mediate  Inference 98 


CHAPTER  X 


CATEGORICAL    SYLLOGISMS 


§  I.  Illustrations  of  the  Syllogism 

§  2.  Of  Figures 

§  3.  Of  Moods 

^  4.  How  valid  Mocds  are  determined 


99 
100 

lOI 

102 


CONTENTS 


XI 


§    5.  Special  Canons  of  the  Four  Figures      . 

§    6.  Ostensive  Reduction  and  the  Mnemonic  Verses 

§    7.  Another  version  of  the  Mnemonic  Verses 

§    8.  Indirect  Reduction        .        .        •       .  • 

§    9.  Uses  of  the  several  Figures. 

§  10.  Scientific  Value  of  Reduction.  .     . 

§  II.  Euler's  Diagrams  for  the  Syllogism       . 


PAGE 
103 
104 
108 

108 
IIO 

III 

112 


CHAPTER  XI 

ABBREVIATED    AND   COMPOUND    ARGUMENTS 

§  I.  Popular  Arguments  Informal  .         .         •         •         • 

§  2.  The  Enthymeme ' 

§  3.  Monosyllogism,  Poly  syllogism.  Prosyllogism.  Episyllog 

§  4.  The  Epicheirema  •••••• 

§  5.  The  Sorites 

§  6.  The  Antinomy         .  •      ,  •         •         "      •  ' 


;ism 


114 

115 
116 

117 
118 
120 


CHAPTER  XII 

CONDITIONAL    SYLLOGISMS 


§  I .  The  Hypothetical  Syllogism 
§  2.  The  Disjunctive  Syllogism 
§  3.  The  Dilemma  . 


122 
126 
127 


CHAPTER  XIII 

TRANSITION    TO    INDUCTION 

SI    Formal  Consistency  and  Material  Truth        .        "         '        ' 
§  2.  Real    General   Propositions   assert    more   than   is   directly 
known       .         •         •         •      •  • 


132 
133 


r "'"--'iffliiritiiiiTiniiirrift'iiiTffrifl 


Xll 


CONTENTS 


CONTENTS 


Xlll 


/ 


%  3.  Hence,  formally,  a  Syllogism's  Premises  seem  to  beg  the 
Conclusion        ......... 

§  4.  Materially,  a  Syllogism  turns  upon  the  resemblance  of  the 
Minor  to  the  Middle  Term ;  and  thus  extends  the  Major 
Premise  to  new  cases 

§  5.  Restatement  of  the  Dictinn  :  equivalent  to  the  Nota  nota; 

§  6.  Material  Subalternation 

§  7.  Uses  of  the  Syllogism 

§  8.  Materially,  a  Syllogism  trusts  to  the  Uniformity  of  Nature 

§  9.  The  Uniformity  of  Nature  analysed        .... 


CHAPTER  XIV 


CAUSATION' 


§  I.  The  most  important  aspect  of  Uniformity  in  relation  to  In- 
duction is  Causation 

§  2.  Definition  of  "  Cause  "  explained.  The  five  marks  of  Causa- 
tion    

§  3.  How  strictly  the  conception  of  Cause  can  be  applied  depends 
upon  the  subject  under  investigation         .... 

§  4.  Scientific  conception  of  Effect.     Plurality  of  Causes      . 

§  5.  Some  condition,  but  not  the  whole  cause,  may  long  precede 
the  Effect ;  and  some  co-effect,  but  not  the  whole  effect, 
may  long  survive  the  Cause 

§  6.  Mechanical  Causes  and  the  homogeneous  Intermixture  of 
Effects ;  Chemical  Causes  and  the  heteropathic  Inter- 
mixture of  Effects 

§  7.  Tendency,  Resultant,  Counteraction,  Elimination,  Resolu- 
tion, Analysis,  Reciprocity 


CHAPTER  XV 

INDUCTIVE   METHOD 

§  I.  Outline  of  Inductive  investigation  . 

§  2.  Induction  defined     ..... 


PAGE 


135 


136 

137 
138 

138 
140 
141 


145  ^ 

146  — 

153 

155  — 

156  — 
139-^ 


§  3.  "  Perfect  "  Induction 

§  4.  Imperfect  Induction  methodical  or  immethodical  . 

§  5.  Observation  and  Experiment,  the  material  ground  of  Induc- 
tion, compared  ...»••••• 

§  6.  The  principle  of  Causation  is  the  formal  ground  of  Induction 

§  7.  The  Inductive  Canons  are  derived  from  the  principle  of 
Causation,  the  more  readily  to  detect  it  in  facts  observed 


^/ 


CHAPTER  XVI 


THE   CANONS    OF    DIRECT    INDUCTION 

§  I.  The  Canon  of  Agreement 

Negative  Instances  (p.  174) ;  PluraUty  of  Causes  (p.  174) ; 
Agreement  may  show  connection  without  direct  Causa- 
tion (p.  175) 
§  2.  The  Canon  of  Agreement  in  Presence  and  in  Absence  . 
•  It  tends  to  disprove  a  Plurality  of  Causes  (p.  178) 

§  3.  The  Canon  of  Difference 

May  be  applied  to  observations  (p.  183) 

§4.  The  Canon  of  Variations 

How  related  to  Agreement  and  Difference  (pp.  185-6) ; 
The  Graphic  Method  (p.  187) 
§  5.  The  Canon  of  Residues 


PAGH 
165 
166 

167 

168^- 
170— • 


172 


176 
180 
184 

189 


161 
164 


CHAPTER  XVII 

COMBINATION    OF    INDUCTION    WITH    DEDUCTION 

§  I.  Deductive  character  of  Formal  Induction 
§  2.  Further  complication  of  Deduction  with  Induction 
§  3.  The  Direct  Deductive  (or  Physical)  Method  .     f  . 
§  4.  Opportunities  of  Error  in  the  Physical  Method 
§  5.  The  Inverse  Deductive  (or  Historical)  Method     ^ 
§  6.  Precautions  in  using  the  Historical  Method    . 


192 
194 

195 
198 

200 

204 


y 

1/ 


XIV 


CONTENTS 


CHAPTER  XVIII 


HYPOTHESES 

§  I .  Hypothesis  defined  and  distinguished  from  Theory 
Employed  in  common  reasoning  (p.  209) 

§  2.  An  Hypothesis  must  be  verifiable  .  .... 

§  3.  Proof  of  Hypotheses 

(i)  Must  an  hypothetical  agent  be  directly  observable 
(p.  211) ;   Vera  causa  (p.  212) 

(2)  An  Hypothesis  must  be  adequate  to  its  pretensions 
(p.  213)  ;  Exceptio  prohat  regidam  (p.  214) 

(3)  Every    competing    Hypothesis    must    be    excluded 
(p.  215) ;  Crucial  instance  (p.  217) 

§  4.  Hypotheses  necessary  in  scientific  investigation     . 

§5.  The  Method  of  Abstractions 

Method  of  Limits  (p.  222) ;  In  what  sense  all  knowledge 
is  hypothetical  (p.  223) 


PAGE 

208 1. 


210 

211 


218 

221 


CHAPTER  XIX 

LAWS   CLASSIFIED  ;     CO-EXISTENCE  ;    EXPLANATION  ;    ANALOGY 

§  I.  Axioms;    Primary  Laws;    Secondary  Laws,    Derivative  or 

Empirical ;  Facts 225 

§  2.  Secondary  Laws  either  Invariable  or  Approximate  Generali- 
sations      .         ......... 

§  3.  Secondary  Laws  trustworthy  only  in  '  Adjacent  Cases  ' 

§  4.  Secondary  Laws  of  Succession  or  of  Co-existence 

Natural  Kinds  (p.  231),  Co-existence  of  concrete  things 
to  be  deduced  from  Causation  (p.  232) 

§  5.  Explanation  consists  in  tracing  resemblance,  especially  of 
Causation  ........ 

§  6.  Three  modes  of  Explanation 

Analysis  (p.  236) ;   Concatenation  (p.  236) ;  Subsumption 

(P-  237) 
§  7.  Limits  of  Explanation     ....... 

§  8.  Analogy 


228 
229 
231 


234 
236 


238 

240 


CONTENTS 


XV 


CHAPTER  XX 


PROBABILITY 

§  I.  Meaning  of  Chance  and  Probability 

§  2.  Probability  as  a  fraction  or  proportion  . 

§  3.  Probability  depends  upon  experience  and  statistics 

§  4.  It  is  a  kind  of  Induction,  and  pre-supposes  Causation 

§5.  Of  Averages  and  •  Errors ' 

Personal  Equation  (p.  250) ;    meaning  of  '  E.xpectation  ' 
(p.  250) 
§  6.  Rules  of  the  combination  of  Probabilities :     .         .        .         . 

Detection  of  a  hidden   Cause  (p.  251);   oral   tradition 
(p.  252) ;  circumstantial  and  analogical  evidence  (p.  253) 


PAGE 
242 
244 

244 

247' 
249 


251 


CHAPTER  XXI 


DIVISION    AND    CLASSIFICATION       ^ 

§  I .  Classification,  scientific,  special  and  popular  .    -     .         .  254 

§  2.  Uses  of  classification 256 

§3.  Classification,  Deductive  and  Inductive         ....  257' 

§  4.  Division,  or  Deductive  Classification  :  its  Rules    .         .         .  258 

§  5    Rules  for  testing  a  Division 260 

§  6.  Inductive  Classification 261 

§7.  Difficulty  of  Natural  Classification 262 

§  8.  Darwin's  influence  on  the  theory  of  Classification  264 
§  9.  Classification  of  Inorganic  Bodies  also  dependent  on  Causa- 
tion    267 


CHAPTER  XXII 


NOMENCLATURE  ;     DEFINITION  ;     PREDICABLES 

§    I.  Precise  thinking  needs  precise  language 

§    2.  Nomenclature  and  Terminology 

in  popular  Language  (p.  272) 

§    3^.  Definition 

§    4.  Rules  for  testing  a  Definition 


269 
270 

272 
273 


XV] 


CONTENTS 


1         J 


1 
)  > 
>     > 

>    5    5 


§    5.  Every  Definition  is  relative  to  a  Classification 
§    6.  Difficulties  of  Definition        .... 

Proposal  to  substitute  the  Type  (p.  276) 
§    7.  The  Limits  of  Definition       .... 
§    8.  The  five  Predicables 

Porphpyry's  Tree  (p.  280) 
§    9.  Realism  and  Nominalism       .... 
§  10.  The  Predicaments  .... 


CHAPTER  XXIII 

DEFINITION    OF    COMMON    TERMS 

§  I    The  rigour  of  scientific  method  must  be  qualified  . 
§  2.  Still,  Language  comprises  the  Nomenclature  of  an  imperfect 
Classification,  to  which  every  Definition  is  relative ; 

§  3.  and  an  imperfect  Terminology 

§  4.  Maxims  and  precautions  of  Definition 

§  5.  Words  of  common  language  in  Scientific  use         .         .         . 
§  6.  How  Definitions  affect  the  cogency  of  arguments 


CHAPTER  XXIV 

FALLACIES 

§  I.  Fallacy  defined  and  divided    . 
§  2.  Formal  Fallacies  of  Deduction 
§  3.  Formal  Fallacies  of  Induction 
§  4.  Material  Fallacies  classified    . 
§  5.  Fallacies  of  Observation 
§  6.  Begging  the  Question 
§  7.  Surreptitious  Conclusion 

§  8.  Ambiguity • 

§  9.  Fallacies,  a  natural  rank  growth  of  the  Human   Mind,  not 
easy  to  classify,  or  exterminate 

Questions 


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>    3 


CHAPTER   I 


INTRODUCTORY 


§  I.  Logic  is  the  science  that  explains  what  conditions 
must  be  fulfilled  in  order  that  a  proposition  may  be  proved, 
if  it  admits  of  proof.  Not,  indeed,  every  such  proposition  ;  for 
as  to  those  that  declare  the  equality  or  inequality  of  numbers 
or  other  magnitudes,  to  explain  the  conditions  of  their  proof 
belongs  to  Mathematics:  they  are  said  to  be  quantitative. 
But  as  to  all  other  propositions,  called  qualitative^  like  most 
of  those  that  we  meet  with  in  conversation,  in  literature,  in 
politics,  and  even  in  the  sciences  that  are  not  treated  mathe- 
matically (say,  Botany  and  Psychology);  propositions  that 
merely  tell  us  that  something  happens  (as  that  salt  dissolves  in 
ivater\  or  that  something  has  a  certain  property  (as  that  the 
east  wind  is  batieful),  or  that  something  is  related  to  a  class  of 
things  (as  that  Englishmen  are  good  sailors) :  as  to  these,  it 
belongs  to  Logic  to  show  how  we  may  judge  whether  they  are 
true,  or  false,  or  doubtful.  When  propositions  are  expressed 
with  the  universaHty  and  definiteness  that  belongs  to  scientific 
statements,  they  are  called  laws  ;  and  laws,  so  far  as  they  are 
not  laws  of  quantity,  are  tested  by  the  principles  of  Logic,  if 
they  at  all  admit  of  proof. 

But  it  is  plain  that  the  process  of  proving  cannot  go  on  for 
ever ;  something  must  be  taken  for  granted  ;  and  this  is  usually 
considered  to  be  the  case  with  those  highest  laws  that  are 
called  axioms  or  first  principles,  of  which  we  can  only  say  that 
we  know  of  no  exceptions  to  them,  that  we  cannot  help 
believing  them,  and  that  they  are  indispensable  to  science  and 

A 


•  • 


•    « 


•     •  •••  t 

••     •  •     •  ••  • 

•  •    •    •••  •«, 

,       •••••• 


'•  •  • 


•    • 


»  •    ••  • 


as 


,?....l.€lGi<3!:-J3EDWi;iVE  AND   INDUCTIVE 

•  ;•••  •  I  #.2   •   •  ••  •  •• 

t(5  consistent  thou^ht^     J^ogic,  then,  may  be  briefly  defined 

the  3:(;;ef\Ce.*(5f  Sf^l^  witlj  respect  to  qualitative  laws  and  propo- 
sitioirs,  ^^fc'ept  \hose  tnat  are  axiomatic. 

§  2.  Proof  may  be  of  different  degrees  or  stages  of  com- 
pleteness. Absolute  proof  would  require  that  a  proposition 
should  be  shown  to  agree  with  all  experience  and  with  the 
systematic  explanation  of  experience,  to  be  a  necessary  part 
of  an  all-embracing  and  self-consistent  philosophy  or  theory  of 
the  universe ;  but  as  no  one  hitherto  has  been  able  to  frame 
such  a  philosophy,  we  must  at  present  put  up  with  something 
less  than  absolute  proof.  Logic,  assuming  certain  principles 
to  be  true  of  experience,  or  at  least  to  be  conditions  of  con- 
sistent discourse,  distinguishes  the  kinds  of  propositions  that 
can  be  shown  to  agree  with  these  principles,  and  explains  by 
what  means  the  agreement  can  best  be  exhibited.  These 
principles  will  be  found  in  chaps,  vi.,  ix.,  xiii.,  xiv.  To  bring  a 
proposition  or  an  argument  under  them,  or  to  show  that  it 
agrees  with  them,  is  logical  proof. 

The  extent  to  which  proof  is  requisite,  again,  depends  upon  circum- 
stances ;  whether  our  aim  be  general  truth  for  its  own  sake,  or  merely 
to  compare  a  proposition  with  our  own  convictions,  or  to  satisfy  the 
doubts  of  a  friend.  If  A  and  B  are  conversing,  and  A  asserts  that  some 
white  races  have  straight  black  hair,  and  B  doubts  this,  but  is  willing  to 
grant  that  some  races  n'ith  straight  black  hair  are  ivhite,  A  may  perhaps 
prove  his  point  to  the  satisfaction  of  B  by  showing  that  these  two  pro- 
positions are  intrinsically  the  same,  as  only  differing  in  the  order  of  the 
words.  This  is  called  proof  by  Immediate  Inference,  or  by  e(4uivalence 
of  meaning. 

Again,  if  B  is  ready  to  admit  that  the  Basques  and  Finns  are  white 
races,  and  that  they  also  have  straight  black  hair,  then,  when  A  puts 
these  two  propositions  together  thus — 

The  Basques  and  Finns  have  straight  black  hair  ; 

The  Basques  and  Finns  are  white  races  ; 

Therefore,  some  white  races  have  straight  black  hair — 
the  truth  of  the  last  proposition  is  not  likely  to  be  disputed  any  longer. 
And  this  is  called  proof  by  Mediate  Inference ;  that  is  to  say,  a  con- 
nection between  '  some  white  races  '  and  *  straight  black  hair '  is  sup- 
posed not  to  be  directly  perceivable,  but  to  be  discovered  by  finding  that 
both  are  connected  in  a  certain  way  with  '  Basques  and  Finns. ' 

If,  however,  B  does  not  grant  that  the  Basques  or  the  Finns  are  a 


INTRODUCTORY  3 

vvhite  race,  or  that  they  have  straight  black  hair,  and  A  tries  to  prove 
these  propositions,  his  difficulties  greatly  increase  and  may  become 
msuperable.  He  must  collect  ethnological  evidence,  and  convince  B  of 
Its  sufficiency  ;  and  if  his  friend  be  of  a  sceptical  turn  of  mind,  or  desire 
a  reputation  for  ingenuity  rather  than  for  good  sense,  the  conclusion 
that  some  white  races  have  straight  black  hair  may  be  indefinitely  postponed 
In  fact,  to  follow  out  this  illustration  would  be  altogether  unsuitable  to 
an  introductory  chapter  ;  we  had  better  turn  to  a  simpler  case 

Suppose  that  A  holds  in  his  hand  a  piece  of  yellow  metal,  which  he 
asserts  to  be  copper,  and  that  B  doubts  this,  perhaps  suggesting  that  it 
IS  really  gold.  Then  A  may  propose  to  dip  it  in  vinegar  ;  and  we  will 
suppose  B  to  agree  that,  if  it  then  turns  green,  it  is  copper  and  not  gold 
On  trying  this  experiment  the  metal  does  turn  green  ;  so  that  we  may 
put  A  s  argument  in  this  way  ;— 

IVhatever  yellow  metal  turns  green  in  vinegar  is  copper  ; 
This  yellow  metal  turns  green  in  vinegar ; 
Therefore,  this  yelloiv  metal  is  copper. 
Now.  however,  it  may  occur  to  B  that  the  liquid  in  which  the  metal 
was  dipped  was  not  vinegar,  or  not  pure  vinegar,  and  that  the  greenness 
was  due  to  the  impurity.     A  must  thereupon  show  by  some  means  that 
the   vinegar   was   pure ;    and   then   his  argument  will   be  that    since 
nothing  but  the  vinegar  came  in  contact  with  the  metal,  the  greenness 
was  due  to  the  vinegar ;    or,   in  other  words,   that   contact  with  the 
vinegar  was  the  cause  of  the  metal  turning  green. 

Still,  on  second  thoughts.  B  may  suspect  that  he  had  formerly  con- 
ceded too  much  ;  he  may  reflect  that,  although  it  had  often  been  shown 
that  copper  turned  green  in  vinegar,  whilst  gold  did  not.  yet  the  same 
niight  not  always  happen.  How  do  we  know,  he  may  ask.  that  just  at 
this  moment,  and  perhaps  always  for  the  future  gold  turns,  and  will 
turn  green  in  vinegar,  whilst  copper  does  not  and  never  will  again  ? 
A  will  probably  reply  that  this  is  to  doubt  the  uniformity  of  causation- 
he  may  hope  that  B  is  not  serious  :  he  may  point  out  to  his  friend  that 
in  every  action  of  his  life  he  takes  such  uniformity  for  granted.  But  he 
will  be  obliged  to  admit  that,  whatever  he  may  say  to  induce  his  friend 
to  assent  to  the  principle  of  Nature's  uniformity,  his  arguments  will  not 
amount  to  logical  proof,  because  every  argument  in  some  way  assumes 
that  principle.  He  has  come,  in  fact,  to  the  limits  of  Logic  Just  as 
the  mathematician  does  not  try  to  prove  that  •  two  magnitudes  equal  to 
the  same  third  are  equal  to  one  another.'  so  the  Logician  (as  such)  does 
not  attempt  to  prove  the  uniformity  of  causation  and  the  other  orin 
ciples  of  his  science.  ^ 

§  3-  Two  departments  of  Logic  are  usually  recognised.  De- 
duction and  Induction ;  that  is,  to  describe  them  briefly,  proof 
from  principles,  and  proof  from  facts.  *  Classification  is' some- 


4  LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

times  made  a  third  department;    sometimes  its  topics  are  dis- 
tributed  amongst  those  of  the   former  two.     In  the  present 
manual  the  order  adopted  is,  Deduction,  in  chaps,  ii.  to  xiii.  ; 
Induction  in  chaps,  xiii.  to  xx. ;  and  lastly.  Classification.    This 
order  has  been  followed  partly  from  some  real  convenience  it 
has,  partly  in  deference  to  custom  ;  but  no  formal  division  of 
the  subject  has  here  been  made  into  parts  or  books,  because 
(however   convenient    such   a   grouping   may   be   in  a  larger 
treatise)  it  seemed  desirable  to  avoid  giving  students  the  im- 
pression that  such  divisions  represent  fundamentally  distinct 
and  opposed  aspects  of  the  science.     Although  in  discussing 
any  question  with  an  opponent  who  makes  admissions,  it  may 
be  posssible  to  combat  his  views  with  merely  deductive  argu- 
ments based    upon    his   admissions;    yet   in  any  question    of 
general  truth,  induction  and  deduction  are  mutually  dependent 
and  imply  one  another. 

This  may  be  seen  in  one  of  the  above  examples.  A  argues  that  a 
certain  metal  is  copper,  because  every  metal  is  copper  that  turns  green 
when  dipped  in  vinegar.  So  far  his  proof  appeals  to  a  general  proposition, 
and  is  deductive.  But  if  B  asks  how  he  knows  the  general  proposition 
to  be  true,  A  alleges  experiments  or  facts ;  and  this  is  inductive  evi- 
dence. Deduction  then  depends  on  Induction.  But  when  B  asks, 
again,  how  any  number  of  past  experiments  can  prove  a  general  pro- 
position, which  must  be  good  for  the  future  as  well  as  for  the  past,  A  in- 
vokes the  uniformity  of  causation  ;  that  is,  he  appeals  to  a  principle, 
and  that  is  again  deductive  proof.  Induction  then  depends  upon 
Deduction. 

We  may  put  it  in  this  way  :  Deduction  depends  on  Induc- 
tion, if  general  propositions  are  only  known  to  us  through  the 
facts.  Induction  depends  on  Deduction  ;  because  one  fact  can 
never  prove  another,  except  so  far  as  what  is  true  of  the  one 
is  true  of  the  other  and  of  any  other  of  the  same  kind ;  and 
because,  to  exhibit  this  resemblance  of  the  facts,  it  must  be 
stated  in  a  general  proposition. 

§  4.  The  use  of  Logic  is  often  disputed :  those  who  have 
not  studied  it,  often  feel  confident  of  their  ability  to  do  without 
it;  those  who  have  studied  it,  are  sometimes  disgusted  with 


INTRODUCTORY 


As  to  those  who,  not  hav  ^  i^f t  '  """""f' '^^'^''^• 
there  will  be  time  enough  to  Sfscuss  ts  „ ^  f"'  '^'  ^  ^'^'''  ''' 
they  know  soniething  abouMt  "nd  a  Ti  ^u'"'  ^^'''^" 
studied  it,  turn  away  in  d  1st    fh        Z  '  ^''°'  ''^^''"S 

able  to  judge  whethef  thev  '  ,'^'  ''"'^^'"  ^^"'  himself  be 

juu^c  wnetner  they  are  justified,  when  he  hr,«  nffo*     ^ 

to  equal   proficiency  in  the  subiect      Af.       km       !  '^^ 

ing  considerations    may    be   oS    f'T^''^  ^^^  ^^"«- 
severe:  ^  inducements  to   per- 

00  Logic   states,  and   partly  exnhin^;  nr./\  r 

abstract  principles  which  ill  o  he"  sci   Ls  l^'r      '  '"'"" 
namely,  the  axioms  above  mentioned  ^  '''"''"  ' 

(^)  By  exercising  the  student  \n  tu^  ^        u       • 

tions.   It  educates  the  power  of  abstract  thnnahf      ^       u 
-son  Logic  is  the  best  propedeutic  tlphi  o  o      :  tha^is  t'o^ 
Metaphysics  and  speculative  Ethics  ' 

and  i  S';":^"""^^' :''"'  «-"  expounded,  is  a  model  of  method 
and  a  d,sc^l,„e  m  close  and  consecutive  thinking.    This  meX' 
Lo^ic  ought  to  possess  in  a  high  degree 

1  re      Observe  .  the  ^wm;/  nature  of  such  evidenrp      t^ 
would     e  absurd  of  the  Logician  to  pretend  to      sru"  ti 
Chem,st,  Economist  and  Merchant,  as  to  the  ./../,  "char'tr 
o     he  evidence  requisite  in  their  several  spheres  oHudgne  t 
S  .11,  by  investigating  the  general  conditions  of  proo    he  1.^ 
every  man  upon  his  guard  against  insufficient  evi.l"' 

reaso,rWe'  I     '"  '°"  "°^'  '"  "'^  «^^'  P'^^'  ^-^h  us  to 
reason.     We  learn  to  reason,  as  we  learn  to  walk  and  t.ll 

by  the  nautral  growth  of  our  powers,  with  some  assfst  nc^; 
from    nends  and  neighbours.     But,  to  be  frank,   f^w  of  u 

L  go        tail"""."""''"^  '''''■'  ^"'^'  -  '°  ---ng 
Logic  cettamly  quickens  our  sense  of  bad  reasoning,   bott 


6  LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

in  others  and  in  ourselves.  It  helps  us  to  avoid  being  misled 
by  others,  and  to  correct  our  own  mistakes.  A  man  who 
reasons  deliberately,  manages  it  better  after  studying  Logic 
than  he  could  before— if  he  tries  to,  if  he  has  not  a  perverse 
liking  for  sophistry,  and  if  he  has  the  sense  to  know  when 
formalities  are  out  of  place.  There  are  some  mental  qualities 
that  a  man  can  only  get  from  his  father  and  mother. 

(<?)  One  application  of  the  science  of  proof  deserves  special 
mention  :  I  mean,  to  that  department  of  Rhetoric  that  has 
been  the  most  developed,  relating  to  persuasion  by  means  of 
oratory,  leader-writing,  or  pamphleteering.  It  is  usually  said 
that  Logic  is  useful  to  convince  the  judgment,  not  to  persuade 
the  will :  but  one  way  of  persuading  the  will  is  to  convince  the 
judgment  that  a  certain  course  is  advantageous;  and  although 
this  is  not  always  the  readiest  way,  it  is  the  most  honourable, 
and  leads  to  the  most  enduring  results.  Logic,  in  fact,  is  the 
backbone  of  Rhetoric. 

Now,  it  is  in  view  of  these  last  four  uses  of  Logic  (/;,  c,  d,  e) 
that  it  may  be  treated  as  an  Art.  As  a  science,  it  explains  the 
relations  of  truths  to  one  another,  especially  to  certain  first 
principles :  as  an  Art,  it  regards  l>uth  as  an  end  desired,  and 
points  out  some  of  the  means  of  attaining  it;  namely,  to 
proceed  by  a  regular  method,  to  test  any  proposition  by 
the  principles  of  Logic,  and  to  distrust  whatever  cannot  be 
made  consistent  with  them.  It  does  not  give  any  one 
originality  and  fertility  of  invention;  but  it  enables  us  to 
check  our  inferences,  revise  our  conclusions,  and  chasten 
the  vagaries  of  ambitious  speculation.  On  account  of  this 
corrective  function,  Logic  is  sometimes  called  a  Regulative 
Science. 

(/)  Finally,  Logic  is  at  least  a  refined  mental  exercise.  And 
it  needs  no  telescopes,  microscopes,  retorts  or  scalpels;  no 
observatories,  laboratories,  or  museums :  it  is,  therefore,  cheap 
and  convenient.  Moreover,  it  is  of  old  and  honourable 
descent;  a  man  studies  Logic  in  very  good  company.  It 
is  the  warp    upon  which  nearly  the  whole   web  of  ancient, 


INTRODUCTORY  7 

medieval  and  modern  philosophy  has  been  woven;   and  is 
therefore  manifestly  indispensable  to  a  liberal  education. 

§  5.  The  relation  of  Logic  to  other  sciences  may  be  indicated 

thus : 

(^7)  Logic  is  regarded  by  Spencer  as  co-ordinate  with  Mathe- 
matics, both  being  Abstract  Sciences— that  is,  sciences  of  the 
relations  in  which  things  stand  to  one  another,  whatever  the 
^  particular  things  may  be  that  are  so  related;   and  this  view 

seems  to  me  to  be,  on  the  whole,  just— subject,  however,  to 
a  qualification  that  will  appear  presently. 

Mathematics  treats  of  the  relations  of  all  sorts  of  things 
considered   as  quantities,  namely,  as  equal  to,   or  greater,  or 
less  than,  one  another.     Things  may  be  quantitatively  equal 
or   unequal   in   degree,  as   in   comparing  the  temperature   of 
bodies;    or   in    duration;   or    in    spatial  magnitude,    as   with 
lines,  superficies,  solids;   or  in  number.     And  it  is  assumed 
that  the  equality  or  inequality  of  things  that  cannot  be  direcdy 
compared,  may  be  proved  indirectly  on  the  assumption  that 
'  things  equal  to  the  same  thing  are  equal '  &c. 

Logic  also  treats  of  the  relations  of  all  sorts   of  things, 
but  not  as  to  their  quantity.     It  considers  (i)  that  one  thing 
may  be  like  or  unlike  another  in  certain  attributes,  as  that 
a  shark  is  in  many  ways  like  a  ray,  and  in  many  ways  unlike 
a  star-fish  :  (ii)  that  attributes  co-exist  or  coinhere  (or  not)  in 
the  same  subject,  as  the  having  several  rows  of  teeth  and  a 
backbone  prolonged  into  the  upper  lobe  of  the  tail  coinhere 
in  a  shark  :  and  (iii)  that  one  event  follows  another  (or  is  the 
effect  of  it),  as  that  the  placing  of  iron  in  water  causes  it  to 
rust.     The  relations  of  likeness  and  of  coinherence  are  most 
prominent  in  the  department  of  Classification ;   for  it  is  by 
resemblance  of  coinhering  attributes  that  things  form  classes  : 
the  relation  of  succession,  in  the  mode  of  causation,  is  the 
chief  subject  of  the  department  of  Induction.     It  is  usual 
to  group  together  these  relations  of  attributes  and  of  order 
in  time,  and  call  them  qualitative,  in  order  to  contrast  them 
with  the  quantitative  which  belong  to  Mathematics,     And  it  is 


w 


8         LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

assumed  that  qualitative  relations  of  things,  when  they  cannot 
be  directly  perceived,  may  be  proved  indirectly  by  assuming 
the  axiom  of  the  Syllogism  (chap,  ix.)  and  the  law  of  Causa- 
tion (chap.  xiv.). 

So   far,    then,   Logic   and    Mathematics   appear   to   be   co- 
ordinate and  distinct  sciences.     But  we   shall    see   hereafter 
that  the  satisfactory  treatment  of  that  special  order  of  events 
in  time  which  constitutes  Causation,  recjuires  a  combination  of 
Logic  with  Mathematics.     On  the  other  hand.  Logic  may  be 
said  to  be  in  some  respects  'prior  to'  or  *  above'  Mathematics 
as   usually  treated.     For  the  Mathematics   assume   that   one 
magnitude  must  be  either  equal  or  unequal  to  another,  and 
that  it  cannot  be  both  equal  and  unequal  to  it,  and   thus 
take  for  granted  the  principles  of  Contradiction  and  Excluded 
Middle;  but  the  statement  and  elucidation  of  these  principles 
is  left  to  Logic  (chap,  vi.)     The  Mathematics  also  classify  and 
define  magnitudes,  as  (in  Geometry)  triangles,  squares,  cubes, 
spheres;   but    the   principles    of  classification  and  definition 
remain  for  Logic  to  discuss. 

(/>)  As   to    the    concrete    Sciences,    such    as    Astronomy, 
Chemistry,  Zoology,  Politics— Logic  (as  well  as  Mathematics) 
is  implied  in  them  all;  for  all  the  propositions  of  which  they 
consist    involve   causation,    coexistence,    and    class-likeness. 
Logic  is  therefore  said  to  be  prior  to  them  or  above  them  : 
meaning  by  *  prior  '  not  that  it  should  be  studied  earlier,  for 
that  is  not  a  good  plan ;  meaning  by  *  above '  not  in  dignity, 
for  distinctions  of  dignity  amongst  liberal  studies  are  absurd.' 
But  it  is  a  philosophical  idiom  to  call  the  abstract  '  prior  to,' 
or  'higher  than,'  the  concrete    (see    Porphyry's    Tree,   chap, 
xxii.  §  8) ;  and  Logic  is    more   abstract  than  Astronomy  or 
Politics.     Philosophy  may  thank  that  idiom  for  many  a  foolish 
notion. 

(c)  But,  as  we  have  seen.  Logic  does  not  investigate  the  truth, 
trustworthiness,  or  validity  of  its  own  principles;  nor  does 
Mathematics :  this  task  belongs  to  Metaphysics,  the  criticism 
of  knowledge  and  beliefs. 


INTRODUCTORY  9 

Logic  assumes,  for  example,  that  things  are  what  to  a  careful 
scrutiny  they   seem   to   be ;  that   animals,   trees,    mountams, 
planets,  are  bodies  with  various  attributes,  existing  m  space 
and  changing  in  time;  and  that   certain   principles,   such   as 
Contradiction  and  Causation,  are  true  of  things  and  even  s. 
But  Metaphysicians  have  raised  many  plausible  obje^ctions  to 
these  assumptions.     It  has  been  urged  that  natural  objects  do 
not  really  exist  on  their  own  account,  but  only  in  dependence 
on  some  mind  that  contemplates  them,  and  that  even  space 
and  time  are  only  our  way  of  perceiving  things  ;  or,  again,  that 
although  things  do  really  exist  on  their  own  account,  it  is  in  an 
entirely  different  way  from  that  in  which  we  know  them.     As 
to  the  principle  of  Contradiction-that  if  an  object  has  an 
attribute,   it  cannot  at   the  same  time  and  in  the  same  way 
be  without  it  (..A^,  if  an  animal  is  conscious,  it  is  false  that  it 
is  not  conscious)-it  has  been  contended  that  the  speciousness 
of  this  principle  is  only  due  to  the  narrowness  of  our  minds  or 
even  to  the  poverty  of  language,  which  cannot  make  the  fine 
distinctions  that  exist  in  Nature.     And  as  to  Causation    it  is 
sometimes   doubted   whether    events    always    have    ph>^ical 
causes ;  and  it  is  often  suggested  that,    granting   they   have 
physical  causes,  yet  these  are  such  as  we  can  neither  perceive 
nor  conceive ;  belonging  not  to  the  order  of  nature  as   we 
know  it  but  to  the  secret  inwardness  and  reality  of  Nature 
to  the  wells  and  reservoirs  of  power,    not   to   the   spray   of 
the  fountain  that    glitters    in   our    eyes-'  occult    causes,     in 
short       Now   these   doubts  ^nd   surmises   are   metaphysical 
spectres   which  it    remains    for    Metaphysics    to   lay.     Logic 
has  no  direct  concern  with  them  (although  of  course  meta- 
nhvsical    discussion  is  usually  expected   to    be    logical),  bu. 
keeps   the  plain  path  of  plain   beliefs,   level   with   the  com- 
prehension  of   plain   men.      Metaphysics,    as   examining   the 
grounds  of  Logic  itself,  is  sometimes  regarded  as    the  higher 

°S  The  relation  of  Logic  to  Psychology  will  be  discussed  in 
the  next  section. 


'°       I^OGIC:    DEDUCTIVE   AND   INDUCTIVE 

tru?intrent';"t"  ''""'"'  ""'"''"^  °"'  ''^^  -"^itions  of 
with     )  Ethic,  •;''  °"'"  ^P'^*^")'  ^-"^"'^   i»   — dinate 

right  Iduc  ;  T"  .'7'  "  ^"'^"'"^  'he  conditions  of 
Jn  n.^h  '  -1  "'"^  <">  -■'■^"^^"■^^'  considered  as  deter- 
niimng  the  pnncples  of  criticism  and  good  taste. 

rectms  d  Vn'""r'  ^''°°'^  "'  ''°Sicians  are   commonly 

differ  to' «hr;';i;h.T"^'"^"'^'' •^-'^  ^'•^'-''^"■^'' "■•- 

nalists  sav°    o7  h  "^"  "'''''"y  "''^''"^  "^^  »he  Nomi- 

the  ■Mat:?i;,is^     "SLn's 'o^ ^7'^''''  i"'  ''°"«'^' '  ^ 
these  positions  author  r  ''"'  "'  ^''^^  '"  '""«'«»« 

have  the     e"   ^  s  ^ Z  k'/  ""'^  °'  "i^'"  ""^  """^  "^S'-'^-^' 

"7 -t  ,ater  ^^reStl^dT rtr^  "'^  ^  ^■•-•"- 

sc!:  crtd"^:t":?t'°""  '""-'r""' '-''''''  ^-^^^  -  -^^ 

ana    Art   of   Reasoning,   but   at  the   same   time   is 

shai"    ulthf  T"  "^°^<^"^°des  of  statement  which 

he  u"i  c   iT'"^' '■' "'  '"«""^"''  ""  --«'-  "hat  may  be 
•  uc  buoject  under  discussion      Thu^  ,'f  ^^ //  /r  /  7 ,  , , 

mm  „„v,»,r  nf,^  '  °""''  inference  /'v  the 

\  A    7        "^ '■'^''"'■"" '  '■>"d  «]ually  sound  is  the  inference 

i  he   latter   propos.fon    may   be    false,    but   it   follows  •    and 
tsistnf  '°  ''?  '°"""'^)  '■°^"'^  ■•^  ->•  concerned    V  th  t  e 

=::T;;e:tirz;ot;™'^  °^  '-'^^^  °^  -  — •■ 

(^)  Hamilton,  our  best-known  Conceptualist,  regards  I  ode 
as   the   scence  of  the    "formal   laws   of  thought  "  and  '^f    ■ 
thought   as   thought"   thnt   io       -.i  "  °' 

thought  about.     Just  a    Whl,  .  7"'  '°  "^'^  """^^ 

merdy  with  co^e,  t  flrn  ,  f  '  ''^"■'''  ''"^'c  as  concerned 
as  concerned reiT^;/.!''''^'-'"^'^"'' -  "»-'■'-  '-'s  it 
This  doctrine  TcaLd  Cone   "TT'  u  '''""''  °'  "^°"ght. 

element  of  .houg.:t  s^he  C  ncm  th.  """  u''  ^™^'^^' 
such  as  is  signified  bv  the  '  "'  ""  "^''^""^  '"^'^' 


INTRODUCTORY 


11 


{ 


attributes  common  to  any  class  of  things.  Men,  planets 
colours,  virtuous  actions  or  characters,  have,  severally,  some- 
thing in  common  on  account  of  which  they  bear  these  general 
names  ;  and  the  thought  of  what  they  have  in  common  as  the 
ground  of  these  names  is  a  Concept.  To  affirm  or  deny  one  con- 
cept of  another,  as  S^me  men  are  virtuous.  No  man  u  perfectly 
virtuous  Mo  form  a  judgment,  corresponding  to  the  ProposUions 
of  which  the  other  schools  of  Logic  discourse.  Conceptuahsm, 
then   investigates  the  conditions  of  consistent  judgments. 

To  distinguish  Logic  from  Psychology  is  most  important  m 
connection   with   Conceptualism.     Concepts   and    Judgments 
being  mental  acts,  or  products  of  mental  activity,  it  is  often 
thought  that  Logic  must  be  a  department  of  Psychology.     It 
is  recognised,  of  course,  that   Psychology   deals   with   much 
more   than   Logic  does,  with   sensation,   pleasure   and   pain, 
emotion,  volition ;  but  in  the  region  of  the  intellect,  especially 
in  its  most  deliberate  and  elaborate  processes,   namely,  con- 
ception, judgment,  and  reasoning,  it  is  supposed  that   Logic 
and    Psychology   occupy   some    common   ground.      In   tact, 
however,  the  two  sciences  have  little  in  common  except  a  few 
aeneral  terms,  and  even  these  they  employ  in  different  senses. 
!t  is  usual  to  point  out  that  Psychology  tries  to  explain  the 
subjective   processes  of  conception,  judgment  and  reasoning 
(say,  according  to  the  Laws  of  Association)  and  to  give  their 
natural  history ;  but  that  Logic  is  wholly  concerned  with  the 
results    of    such    processes,    with    concepts,   judgments   and 
reasonings,  and  merely  with  the  validity  of  the  results,  that  is, 
with  their  truth  or  consistency  ;  whilst  Psychology  has  nothing 
to  do  with  their  validity,  but  only  with  their  causes.     Besides, 
the   logical  judgment  is  (in   Formal  Logic  at  least)  quite  a 
different  thing  from  the  psychological :  the  latter  involves  feel- 
ing and  belief,  whereas  the  former  is  merely  a  given  relation 
of  concepts      5  is  P:  that  is  a  model  logical  judgment,  there 
can  be  no  question  of  believing  it ;  but  it  is  logically  valid  if 
M  is  P  and  5  is  M.     If,  again,  belief  has  any  place  in  Logic, 
it  depends  upon  evidence  ;   whereas,  in  Psychology  belief  is 


M 


12        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

shown  to  depend  upon  causes,  which  may  have  evidentiary 
value  or  may  not ;  for  Psychology  explains  quite  impartially 
the  growth  of  scientific  insight  and  the  growth  of  prejudice. 

(r)  Mill,  Bain,  and  Venn,  are  the  chief  Materialist  logicians  ; 

and  to  guard  against  the  error  of  confounding  Materialism  in 

Logic  with  the  ontological  doctrine  that  nothing  exists  but 

Matter,  it   may  suffice  to  remember  that    in  Metaphysics  all 

these  philosophers  are  Idealists.     Materialism  in  Logic  consists 

in  regarding  propositions  as  affirming  or  denying  relations  {cf. 

§  5)  between  matters-of-fact ;  in  treating  the  first  principles  of 

Contradiction  and  Causation  as  true  of  things  so  far  as  they 

are  known  to  us,  and  not  merely  as  conditions  or  tendencies  of 

thought ;  and,  indeed,  in  taking  these  principles  as  conditions 

of  right  thinking,  because  they  seem  to  hold  good  of  Nature. 

To  these  differences  of  opinion  it  will  be  necessary  to  recur 
in  the  next  chapter  (§  4) ;    but  here  I  may  observe  that  it  is 
easy  to  exaggerate  their  importance  in  mere  Logic.     Whoever 
feels  an  interest   in  any  subject   upon  which  opinions  differ, 
knows  how  hard  it  is  not  to  take  sides  about  it.     How  often  in 
pure  science  and  philosophy  we  witness  the  ludicrous  spectacle 
of  partisans  engaging  with  as  much  rancour  as  if  they- were 
politicians  with  the  interests  of  taxation  at  stake  !     If  such  a 
scene  is  ever  witnessed  under  the  dry  light  of  Logic,  let  it  pass 
for  a  bad  dream.    There  is  really  little  at  issue  between  schools 
of  logicians  as  such,  and  as  far  as  their  doctrines  run  parallel ;  it 
is  on  the  metaphysical  grounds  of  their  study,  or  as  to  its 
scope  and  comprehension,  that  they  find  a  battle-field.     As  for 
this  manual,  it  generally  proceeds  upon  the  third,  or  Materialist 
doctrine.     If  Deduction  and  Induction  are  regarded  as  mutu- 
ally dependent  parts  of  one  science,  uniting  the  discipline  of 
consistent  discourse  with  the  method  of  investigating  laws  of 
physical   phenomena,  the    Materialist  doctrine,  that  the  prin- 
ciples of  Logic  are  founded  on  fact,  seems  to  be  the  most 
natural  way  of  thinking.     But  if  the  unity  of  Deduction  and 
Induction  is  not  disputed  by  the  other  schools,  the  Materialist 
may  regard  them  as  allies  exhibiting  in  their  own  way  the  same 


INTRODUCTORY 


13 


A 


body  of  truths.     The  Nominalist  may  certainly  claim  that  his 
doctrine  is  indispensable :    consistently  cogent  forms  of  state- 
ment are  necessary  both   to   the   Conceptualist   and   to   the 
Materialist ;  neither  the  relations  of  thought  nor  those  of  fact 
can  be  arrested  or  presented  without  the  aid  of  language  or 
some   equivalent   system   of  signs.      The  Conceptualist  may 
urge  that  the  Nominalist's  forms  of  statement  and  argument 
exist  for   the  sake  of  their  meaning,  namely,  judgments  and 
reasonings ;  and  that  the  Materialist's  laws  of  Nature  are  only 
judgments  founded  upon  our  conceptions  of  Nature  ;  that  the 
truth   of   observations    and   experiments   depends   upon   our 
powers   of    perception ;  that   perception   is    inseparable    from 
understanding,  and  that  a  system  of  induction  may  be  con- 
structed upon  the  axiom  of  Causation,  regarded  as  a  principle 
of  Reason,  just  as  well  as  by  considering  it  as  a  law  of  Nature, 
and  upon  much  the  same  lines.     The  Materialist,  admitting  all 
this,  may  say  that  the  other  schools  have  not  hitherto  been 
eager  to  recognise  the  unity  of  Deduction  and  Induction  or  to 
investigate   the   conditions    of    trustworthy   experiments    and 
observations  within  the  limits  of  human  understanding ;  that 
thought  is  itself  a  sort  of  fact,  as  complex  in  its  structure,  as 
profound  in  its  relations,  as  subtle  in  its  changes  as  any  other 
fact,  and  therefore  at  least  as  hard  to  know  ;  that  to  turn  away 
from  the  full  reality  of  thought  in  perception,  and  to  confine 
Logic  to  artificially  limited  concepts,  is  to  abandon  the  effort 
to  push  method  to  the  utmost  and  to  get  as  near  truth  as 
possible  ;  and  that  as  to  Causation  being  a  principle  of  Reason 
rather  than  of  Nature,  the  distinction  escapes  his  apprehension, 
since  Nature  seems  to  be  that  to  which  our  private  minds  turn 
upon  questions  of  Causation  for  correction  and  instruction; 
so  that  if  he  does  not  call  Nature  the  Universal  Reason,  it  is 
because  he  loves  severity  of  style. 


k 


4 


%, 


CHAPTER  II 

GENERAL  ANALYSIS   OF   PROPOSITIONS 

§  I.  Since  Logic  discusses  the  proof  or  disproof,  or  (briefly) 
the  testing  of  propositions,  we  must  begin  by  explaining  their 
nature.  x\  proposition,  then,  may  first  be  described  in  the 
language  of  grammar  as  a  sefitence  indicative  ;  and  it  is  usually 
expressed  in  the  present  tense. 

It  is  true  that  other  kinds  of  sentences,  optative,  imperative,  interro- 
gative, exclamatory,  if  they  express  or  imply  an  assertion,  are  not 
beyond  the  view  of  Logic  ;  but  before  treating  such  sentences.  Logic, 
for  greater  precision,  reduces  them  to  their  equivalent  sentences  indi- 
cative. Thus,  /  iLish  it  were  summer  may  be  understood  to  mean.  The 
coming  of  summer  is  an  object  of  my  desire.  Thou  shalt  not  kill  may  be  inter- 
preted as  Murderers  arc  in  danger  of  the  judgment.  Interrogatories,  when 
used  in  argument,  if  their  form  is  affirmative,  have  negative  force,  and 
affirmative  force  if  their  form  is  negative.  Thus,  Do  hypocrites  love 
virtue  ?  anticipates  the  answer,  No.  Are  not  traitors  the  vilest  of  mankind  ? 
anticipates  the  answer.  Yes.  So  that  the  logical  form  of  these  sentences 
is,  Hypocrites  are  not  lovers  of  virtue ;  Traitors  are  the  vilest  of  mankind. 
Impersonal  propositions,  such  as  It  rains,  are  easily  rendered  into  logical 
forms  of  equivalent  meaning,  thus:  Rain  is  falling ;  or,  if  this  be  tauto- 
logy, The  clouds  are  raining.  Exclamations  may  seem  capricious,  but  are 
often  part  of  the  argument.  Shade  of  Chatham  !  usually  means  Chatham, 
being  aware  of  our  present  foreign  policy,  is  much  disgusted.  It  is,  in  fact,  an 
appeal  to  authority,  without  the  inconvenience  of  stating  what  exactly 
it  is  that  the  authority  declares. 

§  2.  But  even  sentences  indicative  may  not  be  expressed 
in  the  way  most  convenient  to  logicians.  SaU  disso/ves  in 
water  is  a  plain  enough  statement  for  ordinary  purposes ; 
but  the  logician  prefers  to  have  it  thus  :  Sa/t  is  soluble  in 
water.     For   he   says    that   a   proposition   is   analy sable   into 


GENERAL  ANALYSIS   OF   PROPOSITIONS      15 

three  elements  :  (i)  a  Subject  (as  Salt)  about  which  something 
is  asserted  or  denied;  (2)  a  Predicate  (as  soluble  in  water) 
which  is  asserted  or  denied  of  the  Subject,  and  (3)  the 
Copula  {is  or  are.,  or  is  not  or  are  not),  the  sign  of  relation 
between  the  Subject  and  Predicate.  The  Subject  and  Pre- 
dicate are  called  the  Terms  of  the  proposition :  and  the 
Copula  may  be  called  the  sign  of  predication,  using  the 
verb  '  to  predicate '  indefinitely  for  either  '  to  affirm  '  or  '  to 
deny.'  Thus  5  is  P  means  the  term  P  is  given  as  related 
in  some  way  to  the  term  S.  We  may,  therefore,  further 
define  a  Proposition  as  *a  sentence  in  which  one  term  is 
predicated  of  another.' 

In  such  a  proposition  as  Salt  dissolves,  the  copula  {is)  is 
contained  in  the  predicate,  and,  besides  the  subject,  only 
one  element  is  exhibited :  it  is  therefore  said  to  be  secundi 
adjacentis.  When  all  three  parts  are  exhibited,  as  in  Salt  is 
soluble,  the  proposition  is  said  to  be  tertii  adjacentis. 

§  3.  The  sentences  of  ordinary  discourse  are,  indeed,  for 
the  most  part,  longer  and  more  complicated  than  the  logical 
form  of  propositions  ;  it  is  in  order  to  prove  them,  or  to  use 
them  in  the  proof  of  other  propositions,  that  they  are  in  Logic 
reduced  as  much  as  possible  to  such  simple  but  explicit  ex- 
pressions as  the  above  {tertii  adjacentis).  A  Compound  Pro- 
position, reducible  to  two  or  more  simple  ones,  is  said  to  be 
exponible. 

The  means  by  which  sentences  are  compounded  may  be  seen  analysed 
in  any  book  of  grammar.  One  of  the  commonest  forms  is  the  copula- 
tive, such  as  Salt  is  both  savoury  and  ivholesome,  equivalent  to  two 
simple  propositions:  Salt  is  savoury;  Salt  is  ivholesomc.  Pure  water 
is  neither  sapid  nor  odorous,  equivalent  to  Water  is  not  sapid;  Water 
is  not  odorous.  Or,  again.  Tobacco  is  injurious,  but  not  when  used  in 
moderation,  equivalent  to  Much  tobacco  is  injurious ;  A  little  ts  not.  (The 
word  but,  however,  sometimes  needs  a  third  proposition  to  bring  out 
its  meaning,  as  in  this  case  :  Other  nations  change,  but  not  the  Chinese — 
an  assertion  of  superiority.) 

Another  form  of  Exponible  is  the  Exceptive,  as  Kladderadatsch  is  pub- 
lished daily,  except  on  week-days,  equivalent  to  Kladderadatsch  is  published  on 
Sunday ;  it  is  not  published  any  other  day.      Still  another  Exponible  is  the 


/ 


i6        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

Exclusive,  as  Only  men  use  /ire,  equivalent   to  Men  arc  users  of  fire ;  No 
other  animals  are. 

There  are  other  compound  sentences  that  are  not  exponible,  since, 
though  they  contain  two  or  more  verbal  clauses,  the  construction  shows 
that  these  are  inseparable.  Thus,  //  cats  arc  scarce,  mice  are  plentiful, 
contains  two  verbal  clauses ;  but  //  cats  are  scarce  is  conditional,  not 
indicative;  and  mice  are  plentiful  is  subject  to  the  condition  that  cats  are 
scarce.  Hence  the  whole  sentence  is  called  a  Conditional  Proposition. 
For  the  various  forms  of  Conditional  Propositions  see  chap.  v.  §  4. 

But,  in  fact,  to  find  the  logical  force  of  recognised  grammatical  forms 
is  the  least  of  a  logician's  difficulties  in  bringing  the  discourses  of  men 
to  a  plain  issue.  Metaphors,  epigrams,  innuendos  and  other  figures  of 
speech  present  far  greater  obstacles  to  a  lucid  reduction  whether  for 
approval  or  refutation.  No  rules  can  be  given  for  finding  everybody's 
meaning.  The  poets  have  their  own  way  of  expressing  themselves  ; 
sophists,  too,  have  their  own  way.  And  the  point  often  lies  in  what  is 
unexpressed.  Thus,  "  barbarous  nations  make,  the  civilised  write  his- 
tory," means  that  civilised  nations  do  not  make  history,  which  none  is 
so  brazen  as  openly  to  assert.  Or  again,  "  Alcibiades  is  dead,  but  X  is 
still  alive."  The  whole  meaning  of  this  '  Exponible  '  is  that  X  would 
be  the  lesser  loss  to  society.  Even  an  epithet  or  a  suffix  implies  a  pro- 
position.    This  personage  may  mean  A'  is  a  pretentious  nobody. 

How  shall  we  discover  such  illusive  predications  except  by  cultivating 
our  literary  perceptions  ?  The  obtuse  man  who  misses  the  meaning 
of  an  epigram  may  escape  some  pain  ;  but  '  the  higher  pain  '  is  good 
for  him.  At  any  rate,  to  disentangle  the  compound  propositions,  and 
to  expand  the  abbreviations  of  literature  and  conversation,  is  a  useful 
logical  exercise.  And  if  it  seem  a  laborious  task  thus  to  reduce  to  its 
logical  elements  a  long  argument  in  a  speech  or  treatise,  it  should  be 
observed  that,  as  a  rule,  in  a  long  discourse  only  a  few  sentences  are  of 
principal  importance  to  the  reasoning,  the  rest  being  explanatory  or 
illustrative  digression,  and  that  a  close  scrutiny  of  these  cardinal  sen- 
tences will  frequently  dispense  us  from  giving  much  attention  to  the 
rest. 

§  4.  But  now,  returning  to  ihe  definition  of  a  Proposition 
given  in  §  2,  that  it  is  'a  sentence  in  which  one  term  is 
predicated  of  another/  we  must  consider  what  is  the  import 
of  such  predication.  Foi  the  definition,  as  it  stands,  seems 
to  be  purely  Nominalist.  Is  a  Proposition  nothing  more  than 
a  certain  synthesis  of  words ;  or,  is  it  meant  to  correspond 
with  something  further,  a  synthesis  of  ideas,  or  a  relation  of 
facts  ? 


< 


GENERAL   ANALYSIS   OF   PROPOSITIONS       17 

Conceptualist  logicians,  who  speak  of  Judgments  instead 
of  Propositions,  of  course  define  the  Judgment  in  their  own 
language.  According  to  Hamilton,  it  is  "a  recognition  of  the 
relation  of  congruence  or  confliction  in  which  two  concepts 
stand  to  each  other."  To  lighten  the  sentence,  I  have  omitted 
one  or  two  qualifications  (Hamilton's  Lectures  on  Logic%  xiii.). 
"  Thus,"  he  goes  on,  "  if  we  compare  the  thoughts  water , 
iron^  and  rusting,  we  find  them  congruent,  and  connect  them 
into  a  single  thought,  thus  :  water  rusts  iron — in  that  case  we 
form  a  judgment."  When  a  judgment  is  expressed  in  words, 
he  says,  it  is  called  a  proposition. 

There  seems  at  first  to  be  a  merely  verbal  difference  upon 
this  point  between  the  three  Schools  (chap.  i.  §  6) ;  for 
Whately  begins  by  describing  a  Proposition  as  "a  judgment 
expressed  in  words,"  though  he  prefers  to  define  it  as  "a 
sentence  indicative."  Mill,  again,  defines  it  as  "a  portion  of 
discourse  in  which  a  predicate  is  affirmed  or  denied  of  a 
subject."  {Logic,  Book  I.,  chap.  iv.  §  i.)  But  further 
differences  come  to  light  when  Whately  observes  that  his 
definition  "relates  entirely  to  the  words,"  and  when  Mill 
goes  on  to  inquire  into  the  import  of  propositions.  (Book  I., 
chap,  v.) 

Mill  finds  three  classes  of  propositions  :  (a)  those  in  which 
one  proper  name  is  predicated  of  another ;  and  of  these  Hobbes's 
Nominalist  definition  is  adequate,  namely,  that  a  proposition 
asserts  or  denies  that  the  predicate  is  a  name  for  the  same 
thing  as  the  subject,  as  Tul/y  is  Cicero. 

(b)  Propositions  in  which  the  predicate  means  a  part  (or 
the  whole)  of  what  the  subject  means,  as  Horses  are  ani?nais, 
Man  is  a  rational  animal.  These  are  Verbal  Propositions 
(See  below:  chap.  v.  §  6),  and  their  import  consists  in 
affirming  or  denying  a  coincidence  between  the  meanings 
of  names,  as  The  meaning  of"  animal^  is  part  of  the  ?neaning  of 
'  horse '. 

But  {c)  there  are  also  Real  Propositions,  whose  predicates 
do  not  mean  the  same  as  their  subjects,  and  whose  import 


/  1: 


I  •' 


i8        LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


consists  in  affirming  or  denying  one  of  five  different  kinds 
of  matter  of  fact:  (i)  That  the  subject  exists,  or  does  not; 
as  if  we  say  The  bison  exists^  The  great  auk  is  exti?icf.  (2) 
Co-existence,  as  Ma?i  is  mortal ;  that  is,  the  Imng;  subject  to 
death  coinheres  with  the  qualities  Ofi  account  of  which  we  call 
certai?i  objects  7?ien.  (3)  Succession,  as  The  military  precedes 
the  industrial  regime.  (4)  Causation  (a  particular  kind  of 
Succession),  as  Water  rusts  iron.  (5)  Resemblance,  as  The 
colour  of  this  geranium  is  like  that  of  a  soldier's  coat. 

On  comparing  this  list  of  real  predications  with  the  list 
of  logical  relations  given  above  (chap.  i.  §  5^),  it  will  be 
seen  that  the  two  differ  only  in  this,  that  I  have  there  omitted 
simple  Existence.  In  fact  nothing  simply  exists,  unrelated 
either  in  Nature  or  in  knowledge.  Still,  such  a  proposition 
as  The  bison  exists  may,  no  doubt,  be  used  in  Logic  (subject 
to  interpretation)  for  the  sake  of  custom  or  for  the  sake  of 

brevity. 

Into  the  question  of  the  Import  of  Propositions  it  would 
be  unsuitable  to  enter  further.  This  controversy  really  turns 
upon  a  difference  of  opinion  as  to  the  scope  of  Logic  and 
the  foundations  of  knowledge.  Mill  was  dissatisfied  with 
the  "  congruity "  of  concepts  as  the  basis  of  a  judgment. 
Clearly,  mere  congruity  does  not  justify  belief.  In  the  pro- 
position Water  rusts  iron,  the  concepts  water,  7'ust  and 
iron  may  be  congruous,  but  does  any  one  assert  their  con- 
nection on  that  ground?  in  the  proposition  Murderers  are 
haunted  by  the  ghosts  of  their  victims,  the  concepts  victim, 
murderer,  ghost  have  a  high  degree  of  congruity ;  yet,  un- 
fortunately, I  cannot  believe  it :  there  seems  to  be  no  such 
cheap  defence  of  innocence.  Now,  Mill  held  that  Logic 
is  concerned  with  the  grounds  of  belief,  and  that  the  scope 
of  Logic  includes  Induction  as  well  as  Deduction ;  whereas, 
according  to  Hamilton,  Induction  is  only  Modified  Logic, 
a  mere  appendix  to  the  theory  of  the  "forms  of  thought 
as  thought."  Indeed,  Mill  endeavoured  in  his  Logic  to  probe 
the  grounds  of  belief  deeper  than  the  science  should  pretend 


GENERAL  ANALYSIS   OF   PROPOSITIONS       19 

to  penetrate,  and  Introduced  a  good  deal  of  Metaphysics— 
certainly,  either  too  much  or  not  enough.     But,  at  any  rate, 
his  great  point  was  that  belief,  and  therefore  (for  the  most 
part)   the   Real    Proposition,    is   concerned   not   merely   with 
the  relations  of  words,  or  even  of  ideas  (though,  of  course, 
propositions    are  judgments   expressed   in   words),    but   with 
matters   of  fact;  that    is,   both    propositions   and  judgments 
point  to  something  further,  to  the  relations  of  things  which 
we  can  examine,  not  merely  by  thinking  about  them  (com- 
paring them   in  thought),  but   by  observing   them  with   the 
united    powers    of    thought   and   perception.     This   is   what 
convinces   us   that   water  rusts   iron:   and   the   difficulty   of 
doing  this  is  what  prevents  our  feeling  sure  that  murderers 
are  haunted  by  the  ghosts  of  their  victims.     Hence,  although 
Mill's  definition  of  a  Proposition,  given  above,  is  adequate 
for   propositions   in   general;    yet   that   kind    of    proposition 
(the  Real)  with  regard  to  which  Logic  (in   Mill's  view)  in- 
vestigates the  conditions   of  proof,   may  be   more   explicitly 
and   pertinently   defined   as    'a    predication    concerning    the 
relation  of  matters  of  fact.' 

§  5.  This  leads  to  a  very  important  distinction  to  which 
we  shall  often  have  to  refer  in  subsequent  pages— namely, 
the  distinction  between  the  Form  and  the  Matter  of  a  pro- 
position or  of  an  argument.  The  distinction  between  Form 
and  Matter,  as  it  is  ordinarily  employed,  is  easily  understood. 
An  apple  growing  in  the  orchard  and  a  waxen  apple  on  the 
table  may  have  the  same  shape,  but  consist  of  different 
materials;  two  real  apples  may  have  the  same  shape,  but 
contain  distinct  ounces  of  apple-stuff,  so  that  after  one  is 
eaten  the  other  remains  to  be  eaten.  Similarly,  tables  may 
have  the  same  shape,  though  one  be  made  of  marble, 
another  of  oak,  another  of  deal.  The  form  is  common  to 
several  things,  the  matter  is  peculiar  to  each.  Metaphysicians 
have,  by  analogy,  carried  the  distinction  further :  apples,  they 
say,  may  have  not  only  the  same  outward  shape,  but  the  same 
inward  constitution,  which,  therefore,  may  be  called  the  Form 


20         LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

of  apple-stuff^namely,  a  certain  pulpiness,  juiciness,  sweetness, 
etc. ;  qualities  common  to  all  dessert  apples :  yet  their  matter 
is  different,  one  being  here,  another  there— differing  in  place 
or  time,  if  in  nothing  else. 

To  apply  this  distinction  to  the  things  of  Logic :  it  is  easy 
to  see  how  two  Propositions  may  have  the  same  Form  but 
different  Matter:  not  using  'Form'  in  the  sense  of  'shape,' 
but   for  that  which   is   common  to  many  things,   in   contrast 
with  that  which  is  peculiar  to  each.     Thus,  All  7nale  lions  have 
tufted  tails  and  All  ivater  is  liquid  at  ^o""  Fahrenheit,  are  two 
propositions  that  have  the  same  form,  though  their  matter  is 
entirely  different.     They  both  predicate  something  of  the  whole 
of  their  subjects,  though  their  subjects  are  different,  and  so  are 
the  things  predicated  of  them.     Again,   All  male  lions  have 
tufted  tails  and  All  ??iale  lions  have  7nanes,  are  two  propositions 
having  the  same  Form  and  in  their  Subjects  the  same  Matter, 
but  different  Matter  in  their  Predicates.     If,  however,  we  take 
two  such  propositions  as  these  :  All  male  lions  have  manes  and 
Some  jnale  lions  have  manes,  here  the  Matter  is  the  same  in 
both,  but  the  Form  is  different— in   the  former,  predication 
is  made  concerning  every  male  lion  ;  in  the  latter  of  only  some 
male  lions  ;   the  former  is  universal,  the  latter  is  particular. 
Or,  again,   if  we  take  Some  tigers  are  man-eaters  and   Some 
tigers  are  not  man-eaters,  here  too  the  Matter  is  the  same, 
but  the  Form  is  different ;  for  the  former  proposition  is  affirma- 
tive, whilst  the  latter  is  negative. 

§  6.  Now,  according  to  Hamilton  and  Whately,  pure  Logic 
has  to  do  only  with  the  Form  of  Propositions  and  arguments. 
As  to  their  Matter,  whether  they  are  really  true  in  fact,  that  is 
a  question,  they  said,  net  for  Logic,  but  for  experience,  or  for 
the  special  sciences.  But  Mill  desired  so  to  extend  logical 
method  as  to  test  the  material  truth  of  propositions  :  he  thought 
that  he  could  expound  a  method  by  which  experience  itself 
and  the  conclusions  of  the  special  sciences  may  be  examined. 

To  this  method,  however,  some  critics  persistently  object, 
that  the  claim  to  determine  Material  Truth  takes  for  granted 


GENERAL   ANALYSIS   OF   PROPOSITIONS       21 

that  the  order  of  Nature  will  remain  unchanged,  that  (for  ex- 
ample) water  not  only  at  present  is  a  liquid  at  50°  Fahrenheit, 
but  will  always  be  so ;  whereas  (although  we  have  no  reason  to 
expect  such  a  thing)  the  order  of  Nature  may  change — it  is  at 
least  supposable — and  in  that  event  water  may  freeze  at  such  a 
temperature.  On  the  other  hand,  they  urge  that  a  certain 
kind  of  Formal  Truth  may  be  placed  beyond  even  the  suppo- 
sition of  possible  error.  An  apple,  for  example,  is  either  green 
all  over,  or  it  is  not :  if  we  affirm  the  one  alternative  we  must 
deny  the  other  ;  this  is  necessary  to  all  intelligible  use  of 
language  and  to  all  clearness  of  thought.  But  upon  the  ques- 
tion of  material  truth,  as  to  the  apple  being  really  green  all 
over,  a  certain  dubiousness  is  defensible  and  not  undignified. 
For  what,  after  all,  is  meant  by  an  apple  *  green  all  over'?  What 
is  'green'?  To  whom  is  it  green?  Not  to  the  colour-blind.  In  what 
circumstances?  Not  in  the  dark.  Any  matter  of  fact  must  depend 
on  observation,  either  directly,  or  by  inference — as  when  some- 
thing is  asserted  about  atoms  or  ether.  But  observation  and 
material  inference  are  subject  to  the  limitations  of  our  faculties; 
and  however  we  may  aid  observation  by  microscopes  and 
micrometers,  it  is  still  observation ;  and  however  we  may 
correct  our  observations  by  repetition,  comparison  and  refined 
mathematical  methods  of  making  allowances,  the  correction 
of  error  is  only  an  approximation  to  accuracy.  Outside  of 
Formal  Reasoning,  suspense  of  judgment  is  your  only  attitude. 

It  is  not  to  be  supposed  that  such  reflections  did  not  occur 
to  Mill,  though  he  may  have  thought  them  strained  and 
negligible.  Here,  however,  it  seems  to  me  right  to  give  them 
some  weight ;  and  accordingly  prominence  will  be  given  to  the 
character  of  Logic  as  a  Formal  Science.  At  the  same  time  it 
will  be  shown  that  Induction  may  be  included  in  Logic  and 
treated  formally ;  and  it  will  be  assumed  that  logical  forms  are 
only  valuable  so  far  as  tjaey  represent  the  actual  relations  of 
natural  phenomena. 

§  7.  Symbols  are  often  used  in  Logic  instead  of  concrete 
terms,  not  only  in  Symbolic  Logic  where  the  science  is  treated 


t*^ 


22        LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

algebraically  (as  by  Dr.  Venn  in  his  Symbolic  Logic)^  but  in 
ordinary  manuals ;  so  that  it  may  be  well  to  explain  the  use  of 
them  before  going  further. 

It  is  a  common  and  convenient  practice  to  illustrate  logical  doctrines 
by  examples  :  to  show  what  is  meant  by  a  Proposition  we  may  give 
salt  is  soluble,  or  water  rusts  iron  :  the  copulative  exponible  is  exemplified 
by  salt  is  savoury  and  wholesome ;  and  so  on.  But  this  procedure  has  some 
disadvantages  :  it  is  often  cumbrous  ;  and  it  may  distract  the  reader's 
attention  from  the  point  to  be  explained  by  exciting  his  interest  in  the 
special  fact  of  the  illustration.  Clearly,  too,  if  Logic  is  only  formal,  no 
particular  matter  of  fact  can  adequately  illustrate  any  of  its  doctrines. 
Accordingly,  writers  on  Logic  employ  letters  of  the  alphabet  instead  of 
concrete  terms  (say),  X  instead  of  salt  or  instead  of  iron,  and  (say)  Y 
instead  of  so/M^/t'  or  instead  of  rusted  by  water;  and  then  a  proposition 
may  be  represented  by  X  is  Y.  It  is  still  more  usual  to  represent  a 
proposition  by  S  is  {or  is  not)  P,  S  being  the  initial  of  Subject,  and  P  of 
Predicate  ;  though  this  has  the  drawback  that  if  we  argue— S  is  P, 
therefore  P  is  S,  the  symbols  in  the  latter  proposition  no  longer  have 
the  same  significance,  since  the  former  Subject  is  now  the  Predicate. 

Again,  negative  terms  frequently  occur  in  Logic,  such  as  not  water,  or 
7iot  iron,  and  then  if  water  or  iron  be  expressed  by  X,  the  corresponding 
negative  may  be  expressed  by  x  ;  or,  generally,  if  a  capital  letter  stand 
for  a  positive  term,  the  corresponding  small  letter  represents  the 
negative. 

And  as  terms  are  often  compounded,  it  may  be  convenient  to  express 
them  by  a  combination  of  letters  :  instead  of  illustrating  such  a  case  by 
boiling  water  or  water  that  is  boiling,  we  may  write  XY  ,  or,  since  positive 
and  negative  terms  may  be  compounded,  instead  of  illustrating  this  by 
water  that  is  not  boiling,  we  may  write  Xy. 

The  convenience  of  this  is  obvious  ;  but  it  is  more  than  con- 
venient ;  fors  if  one  of  the  chief  uses  of  Logic  is  to  discipline 
the  power  of  abstract  thought,  this  can  be  done  far  more 
effectually  by  symbolic  than  by  concrete  examples ;  and  if  such 
discipline  were  the  only  use  of  Logic  it  might  be  best  to 
discard  concrete  illustrations  altogether,  at  least  in  advanced 
Text-books,  though  no  doubt  the  practice  would  be  too  severe 
for  an  elementary  Manual.  But  on  the  other  hand,  to  teach 
the  practical  applicability  of  Logic  to  the  arguments  and 
proofs  of  actual  life,  or  even  of  the  concrete  sciences,  merely 
symboUc  illustration  may  be  not  only  useless  but  even   mis- 


GENERAL  ANALYSIS   OF   PROPOSITIONS       23 

leading.  When  we  speak  of  politics,  or  poetry,  or  species,  or 
the  weather,  the  terms  that  must  be  used  can  rarely  have  the 
distinctness  and  isolation  of  X  and  Y ;  so  that  the  perfunctory 
use  of  symbolic  illustration  makes  argument  and  proof  appear 
to  be  much  simpler  and  easier  matters  than  they  really  are. 
Indeed,  in  this  connection,  it  is  impossible  to  illustrate  Logic 
sufficiently  :  the  student  who  is  in  earnest  about  the  cogency 
of  arguments  and  the  limitation  of  proofs,  and  is  scrupulous  as 
to  the  degrees  of  assent  that  they  require,  must  constantly  look 
for  illustrations  of  the  science  in  his  own  experience  and  rely 
at  last  upon  his  own  sagacity. 


CHAPTER  III 
OF   TERMS   AND   THEIR   DENOTATION 

§  I.  In  treating  of  Deductive  Logic  it  is  usual  to  recognise 
three  divisions  of  the  subject :  first,  the  doctrine  of  Terms, 
words,  or  other  signs  used  as  subjects  or  predicates ;  secondly, 
the  doctrine  of  Propositions,  in  which  terms  are  combined ; 
and,  thirdly,  the  doctrine  of  the  Syllogism  in  which  proposi- 
tions are  combined  as  the  grounds  of  a  conclusion. 

The  terms  employed  are  either  letters  of  the  alphabet,  or 
the  words  of  common  language,  or  the  technicalities  of  science; 
and  since  the  words  of  common  language  are  most  in  use,  it  is 
necessary  to  give  some  account  of  common  language  as  sub- 
serving the  purposes  of  Logic.  It  has  been  urged  that  we 
cannot  think  or  reason  at  all  without  words,  or  some  substitute 
for  them,  such  as  the  signs  of  algebra;  and  although  this 
opinion  is  too  sweeping,  since  we  draw  many  simple  inferences 
by  means  of  mental  imagery,  and  even  animals  do  so  when 
judging  of  prey,  or  enemies,  or  friends  by  their  scent  or 
by  the  noises  they  make ;  yet  the  more  elaborate  inferences, 
and  especially  the  grouping  and  concatenation  of  inferences, 
which  we  call  reasoning,  seem  to  be  impossible  without 
language  or  some  equivalent  system  of  signs.  It  is  not  merely 
that  we  need  language  to  express  our  reasonings  and  commu- 
nicate them  to  others :  in  solitary  thought  we  depend  on 
words— 'talk  to  ourselves,'  in  fact;  though  the  words  or 
sentences  that  then  pass  through  our  minds  are  seldom  fully 
formed  or  articulated.  In  Logic,  moreover,  we  have  carefully 
to  examine  the  grounds  (at  least  the  formal  and  proximate 


/ 


i 


OV  TERMS   AND   THEIR   DENOTATION        25 

grounus)  of  our  conclusions ;  and  plainly  this  cannot  be  done 
unless  the  conclusions  in  question  are  explicitly  stated  and 
recorded. 

Conceptualists  say  that  Logic  deals  not  with  the  process  of 
thinking  (which  belongs  to  Psychology)  but  with  its  results;  not 
with  conceiving  but  with  concepts ;  not  with  judging  but  with 
judgments.  Is  the  concept  self-consistent  or  adequate,  Logic 
asks;  is  the  judgment  capable  of  proof?  Now,  it  is  only  by 
recording  our  thoughts  in  language  that  it  becomes  possible  to 
distinguish  between  the  process  and  the  result  of  thought.  As 
a  mere  train  of  mental  imagery,  the  act  and  the  product  of 
thinking  would  be  identical  and  equally  evanescent.  But  by 
carrying  on  the  process  in  language  and  remembering  or 
otherwise  recording  it,  we  obtain  a  result  which  may  be  ex- 
amined according  to  the  principles  of  Logic. 

§  2.  As  Logic,  then,  must  give  some  account  of  language,  it 
seems  desirable  to  explain  how  its  treatment  of  language  differs 
from  that  of  Grammar  and  from  that  of  Rhetoric. 

Grammar  is  the  study  of  the  words  of  some  language,  their  classifica- 
tion and  derivation,  and  of  the  rules  of  combining  them  according  to  the 
usage  at  any  time  recognised  and  followed  by  those  who  are  considered 
good  authors.  Composition  may  be  faultless  in  its  grammar,  though 
dull  and  absurd. 

Rhetoric  is  the  study  of  language  with  a  view  to  obtaining  some 
special  effect  in  the  communication  of  ideas  or  feelings,  such  as  pic- 
turesqueness  in  description,  vivacity  in  narrative,  lucidity  in  exposition, 
vehemence  in  persuasion,  or  literary  charm.  Some  of  these  ends  are 
often  gained  in  spite  of  faulty  syntax  or  faulty  logic ;  but  since  the  few 
whom  bad  grammar  saddens  or  incoherent  arguments  divert  are  not 
carried  away  as  they  else  might  be  by  an  unsophisticated  orator.  Gram- 
mar and  Logic  are  necessary  to  the  perfection  of  Rhetoric.  Not  that 
Rhetoric  is  in  bondage  to  those  other  sciences  ;  for  foreign  idioms  and 
such  figures  as  the  ellipsis,  the  anacoluthon,  the  oxymoron  and  the 
hyperbole,  and  violent  inversions  have  their  places  in  the  magnificent 
style ;  but  authors  unacquainted  with  Grammar  and  Logic  are  not 
likely  to  place  such  figures  well  and  wisely.  Indeed,  common  idioms, 
though  both  grammatically  and  rhetorically  justifiable,  both  correct 
and  effective,  often  seem  illogical.  'To  fall  asleep,'  for  example,  is  a 
perfect  English  phrase  ;  yet  if  we  examine  severally  the  words  it  con- 


26        LOGIC:   DEDUCTIVE   AND   INDUCTIVE 


seem 


strange  that 


their  combination  should   rfiean 


sists   of,   it   may 
anything  at  all. 

But  Logic  only  studies  language  so  far  as  necessary  in  order  to  state, 
understand,  and  check  the  evidence  and  reasonings  that  are  usually 
embodied  in  language.  And  good  Logic  is  compatible  with  false  con- 
cords and  inelegance  of  style.  If  any  one  argues  thus:  All  men  is 
animals;  therefore,  some  animals  is  men — the  mode  of  expression  may  be 
deprecated,  bat  we  know  what  he  means,  and  the  argument  is  sound. 

-  §  3.  Terms  are  either  Simple  or  Composite  :  that  is  to  say, 
they  may  consist  either  of  a  single  word,  as  *  Chaucer,'  'civili- 
sation ';  or  of  more  than  one,  as  '  the  father  of  English  poetry,' 
or  *  modern  civilised  nations.'  Logicians  classify  words  accord- 
ing to  their  uses  in  forming  propositions ;  or,  rather,  they 
classify  the  uses  of  words  as  terms,  not  the  words  themselves  ; 
for  the  same  word  may  fall  into  different  classes  of  terms 
according  to  the  way  in  which  it  is  used.  (C/.  Mr.  Alfred 
Sidg  wick's  Distinction  and  the  Criticism  of  Beliefs^  chap,  xiv.) 

Thus  words  are  classified  as  Categorematic  or  Syncategore- 
matic.  A  word  is  Categorematic  if  used  singly  as  a  term 
without  the  support  of  other  words  :  it  is  Syncategorematic 
when  joined  with  other  words  in  order  to  constitute  the 
subject  or  predicate  of  a  proposition.  If  we  say  Venus  is  a 
planet  whose  orbit  is  inside  the  Earth's^  the  subject,  '  Venus,'  is 
a  word  used  categorematically  as  a  simple  term  ;  the  predicate 
is  a  composite  term  whose  constituent  words  (whether  sub- 
stantive, relative,  verb,  or  preposition)  are  used  syncategorema- 
tically. 

Prepositions,  conjunctions,  articles,  adverbs,  relative  pronouns,  in 
their  ordinary  use,  can  only  enter  into  terms  along  with  other  words 
having  a  substantive,  adjectival  or  participial  force  ;  but  when  they  are 
themselves  the  things  spoken  of  and  are  used  substantively  {suppositio 
viaterialis),  they  are  categorematic.  In  the  proposition.  Of  was  used  more 
indefinitely  three  hundred  years  ago  than  it  is  now,  'of  is  categorematic. 
On  the  other  hand,  all  substantives  may  be  used  categorematically  ;  and 
the  same  self-sufficiency  is  usually  recognised  in  adjectives  and  partici- 
ples. Some,  however,  hold  that  the  categorematic  use  of  adjectives 
and  participles  is  due  to  an  ellipsis  which  the  logician  should  fill  up  ; 
that  instead  of  Gold  is  heavy,  he  should  say  Gold  is  a  heavy  metal ;  instead 
of  The  sun  is  shining,  The  sun  is  a  body  shining.     But  in  these  cases  the 


I 


i 


OF  TERMS   AND   THEIR   DENOTATION        2-f 

words  •  metal '  and  '  body  '  are  unmistakable  tautology,  since  '  metal '  is 
implied  in  gold  and  '  body  '  in  sun.  But,  as  we  have  seen,  any  of  these 
kinds  of  words,  substantive,  adjective,  or  participle,  may  occur  syncate- 
gorematically  in  connection  with  others  to  form  a  composite  term. 

§  4.  Terms  may  be  classified,  first,  according  to  what  they 
stand  for  or  denote ;  and  this  is  called  their  Denotation.  In 
this  respect,  the  use  of  a  term  is  said  to  be  either  Concrete 
or  Abstract. 

A  term  is  Concrete  when  it  denotes  a  '  thing ' ;  that  is,  any 
person,  object,  fact,  event,  feeling  or  imagination,  considered 
as  capable  of  having  (or  consisting  of)  qualities  and  a  deter- 
minate existence.  Thus  *  cricket  ball'  denotes  any  object 
having  a  certain  size,  weight,  shape,  colour,  etc.  (which  are  its 
qualities),  and  being  at  any  given  time  in  some  place  and 
related  to  other  objects— in  the  bowler's  hands,  in  a  box,  in  a 
shop  window.  Any  '  feeling  of  warmth,'  has  a  certain  intensity, 
as  pleasurable  or  painful,  occurs  at  a  certain  time,  and  affects 
some  part  or  the  whole  of  some  animal.  An  imagination, 
indeed,  (say,  of  a  fairy)  cannot  be  said  in  the  same  sense  to 
have  locality ;  but  it  depends  on  the  thinking  of  some  man 
who  has  locality,  and  is  definitely  related  to  his  other  thoughts 
and  feelings. 

A  term  is  Abstract,  on  the  other  hand,  when  it  denotes  a 
quality  (or  qualities),  considered  by  itself  and  without  deter- 
minate existence  in  time,  place,  or  relation  to  other  things. 
'Size,'  *  shape,'  'weight,'  'colour,'  'intensity,'  'pleasurableness,' 
are  terms  used  to  denote  such  qualities,  and  are  then  abstract 
in  their  denotation.  -'Weight,'  you  observe,  is  not  something 
with  a  determinate  existence  at  a  given  time;  it  exists  not 
merely  in  some  particular  place,  but  wherever  there  is  a  iieavy 
thing ;  and,  as  to  relation,  at  the  same  moment  it  combines  in 
iron  with  hardness  and  in  mercury  with  liquidity.  In  fact,  a 
quality  is  a  point  of  agreement  in  a  multitude  of  different 
things ;  as  all  heavy  things  agree  in  weight,  all  round  things  in 
roundness,  all  red  things  in  redness;  and  an  abstract  term 
denotes  such  a  point  (or.  points)  of  agreement  among  the  things 


2S        LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

denoted  by  concrete  terms.  Thus  the  use  of  abstract  terms 
results  from  the  analysis  of  concrete  things  into  their  qualities  ; 
and  conversely  a  concrete  term  may  be  viewed  as  denoting  a 
synthesis  of  qualities  in  individual  things.  When  several  things 
agree  in  more  than  one  quality,  there  may  be  an  abstract  term 
denoting  the  union  of  qualities  in  which  they  agree,  but  not 
their  peculiarities ;  as  '  human  nature '  denotes  the  'common 
qualities  of  men,  *  civihsation '  the  common  conditions  of 
civilised  peoples. 

Every  general  name,  if  used  as  a  concrete  term,  has,  or  may 
have,  a  corresponding  abstract  term.  Sometimes  the  concrete  term 
is  modified  to  form  the  abstract,  as  'greedy-greediness.'  'vain- 
vanity  ' ;  sometimes  a  word  is  adapted  from  another  language  as 
'  man-humanity  '  ;  sometimes  a  composite  term  is  used,  as  '  mer- 
cury-the  nature  of  mercury,'  etc.  The  same  concrete  may  have 
several  abstract  correlatives,  as  '  man -manhood,  humanity,  human 
nature  ;  'heavy-weight,  gravity,  ponderosity';  but  in  such  cases 
the  abstract  terms  are  not  used  quite  synonymously  ;  that  is,  they 
imply  different  ways  of  considering  the  concrete. 

Whether  a  word  is  used  as  a  concrete  or  abstract  term  is  in  most 
instances  plain  from  the  word  itself,  the  use  of  most  words  being  pretty 
regular  one  way  or  the  other;  but  sometimes  we  must  judge  by  the 
context.  '  Weight  '  may  be  used  in  the  abstract  for  '  gravity  '  or  in 
the  concrete  for  a  measure  ;  but  in  the  latter  sense  it  is  syncategore- 
matic  (in  the  singular),  needing  at  least  the  article  •  a  (or  the)  weight  ' 
'  Government '  may  mean  '  supreme  political  authority,'  and  is  then 
abstract ;  or,  the  set  of  men  who  happen  to  be  ministers,  and  is  then 
concrete ;  but  in  this  case,  too,  the  article  is  usually  prefixed.  '  The 
life  '  of  any  man  may  mean  his  vitality  (abstract),  as  in  "  Thus  follow- 
ing life  ID  creatures  we  dissect  "  ;  or,  the  series  of  events  through  which 
he  passes  (concrete),  as  in  '  the  life  of  Nelson  as  narrated  by  Southey.' 

It  has  been  made  a  question  whether  the  denotation  of  an 
abstract  term  may  itself  be  the  subject  of  qualities.  Apparently 
'  weight '  may  be  greater  or  less,  *  government '  good  or  bad, 
*  vitality'  intense  or  dull.  But  if  every  subject  is  modified  by 
a  quality,  a  quality  is  also  modified  by  making  it  the  subject  of 
another ;  and,  if  so,  it  seems  then  to  become  a  new  quality : 
'greatness  of  weight,'  'badness  of  government,'  *dulness  of 
vitality.'     Or  if  we  say  '  great  weight,'  '  bad  government,'  '  dull 


OF   TERMS   AND   THEIR   DENOTATION        29 

vitality,'  these  phrases  may  be  regarded  as  denoting  some  con- 
crete experience,  such  as  the  effort  felt  in  lifting  a  trunk, 
disgust  at  the  conduct  of  officials,  sluggish  movements  of  an 
animal  when  irritated.  At  any  rate,  it  is  to  such  concrete 
terms  that  w^e  have  always  to  refer  in  order  fully  to  realise  the 
meaning  of  abstract  terms,  and  thereof,  of  course,  to  under- 
stand any  qualification  of  them. 

§  5.  Concrete  terms  may  be  subdivided  according  to  the 
number  of  things  they  denote  and  the  way  in  which  they  de- 
note them.  A  term  may  denote  one  thing  or  many  :  if  one,  it 
is  called  Singular;  if  many,  it  may  do  so  distributively,  and 
then  it  is  General ;  or,  as  taken  all  together,  and  then  it  is 
Collective  :  one,  then  ;  any  one  of  many  :  many  in  one. 

Among  Singular  Terms,  each  denoting  a  single  thing,  the 
most  obvious  are  Proper  Names,  such  as  Gibraltar  or  George 
Washington,  which  are  merely  marks  of  individual  things  or 
persons,  and  often  form  no  part  of  the  common  language  of  a 
country.  They  are  thus  distinguished  from  other  Singular 
Terms,  which  consist  of  common  words  so  combined  as  to 
restrict  their  denotation  to  some  individual,  such  as,  'the 
strongest  man  on  earth.' 

Proper  Terms  are  often  said  to  be  arbitrary  signs,  because  their  use 
does  not  depend  upon  any  reason  that  may  be  given  for  them.  Gibraltar 
had  a  meaning  among  the  Moors  when  originally  conferred  ;  but  no 
one  now  knows  what  it  was,  unless  he  happens  to  have  looked  it  up  ; 
yet  the  name  serves  its  purpose  as  well  as  if  it  were  "  Rooke's  Nest.'' 
Every  Newton  or  Newport  year  by  year  grows  old.  but  to  alter  the 
name  would  cause  only  confusion.  If  such  names  were  given  by  mere 
caprice  it  would  make  no  difference;  and  they  could  not  be  more 
cumbrous,  ugly,  or  absurd,  than  many  of  those  that  are  given  'for 
reasons.' 

The  remaining  kinds  of  Singular  Terms,  drawn  from  the  common 
resources  of  the  language,  derive  their  denotative  force  from  their  usual 
meanings.  Thus  the  pronouns  'he,'  'she.'  'it.'  are  singular  terms, 
whose  present  denotation  is  determined  by  the  occasion  and  context  of 
discourse:  so  with  demonstrative  phrases— '  this  man,'  'that  horse.' 
Descriptive  names  may  be  more  complex,  as  'the  wisest  man  of 
Gotham.'  which  is  limited  to  some  individual  by  the  superlative  suffix  ; 
or  '  the  German  Emperor,'  which  is  Hmited  by  the  definite  article— the 


fr^^ 


30        LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

general  term  '  German  Emperor  '  being  thereby  restricted  either  to  the 
reignmg  monarch  or  to  the  one  we  happen  to  be  discussing.  Instead 
of  the  definite,  the  indefinite  article  may  be  used  to  make  general  terms 

smgular.  as  •  a  German  Emperor  was  crowned  at  Versailles '  (individua 

vaga).  ^ 

Abstract  terms  are  ostensively  singular:  *  whiteness'  {e.^.) 
is  one  quality.  But  their  full  meaning  is  general :  *  whiteness  ' 
stands  for  all  white  things,  so  far  as  white.  Abstract  terms, 
in  fact,  are  only  formally  singular. 

(General  terms  are  words,  or  combinations  of  words,  used  to 
denote  any  one  of  many  things  that  resemble  one  another  in 
certain  respects.  'CJeorge  III.'  is  a  Singular  Term  denoting 
one  man;  but  *King'  is  a  General  Term  denoting  him  and 
all  other  men  of  the  same  rank  ;  whilst  the  compound  '  crowned 
head '  is  still  more  general,  denoting  kings  and  also  emperors. 
It  is  the  nature  of  a  general  term,  then,  to  be  used  in  the  same 
sense  of  whatever  it  denotes ;  and  its  most  characteristic  form 
is  the  Class-name,  whether  of  objects,  such  as  'king,'  'sheep,' 
'ghost';  or,  of  events  such  as  'accession,'  'purchase,' ^mani- 
festation.' Things  and  events  are  known  by  their  qualities 
and  relations;  and  every  such  aspect,  being  a  point  of  re- 
semblance to  some  other  things,  becomes  a  ground  of  general- 
isation, and  therefore  a  ground  for  the  need  and  use  of  general 
terms.  Hence  general  terms  are  far  the  most  important  sort 
of  terms  in  logic,  since  in  them  general  propositions  are  ex- 
pressed, and,  moreover  (with  rare  exceptions),  all  predicates 
are  general. 

For.  besides  these  typical  class-names,  attributiye  words  are  general 
terms,  such  as  'royal.'  'ruling,'  'woolly,'  'bleating,'  'impalpable.' 
'  yanishing.'  Infinitiyes  may  also  be  used  as  general  terms,  as  "To  err 
is  human  "  ;  but  are  best  translated  into  equivalent  substantive  forms,  as 
Foolish  actions  are  characteristic  of  mankind.  Abstract  terms,  too,  are  fas 
I  observed)  equivalent  to  general  terms  :  '  folly  '  is  abstract  for  '  foolish 
actions.'  '  Honesty  is  the  best  policy  '  means  people  who  are  honest  may  hope 
to  find  their  account  in  being  so;  that  is,  in  the  effects  of  their  honest 
actions,  provided  they  are  wise  in  other  wavs,  and  no  misfortunes  attend 
them.  The  abstract  form  is  often  much  the  more  succinct  and  forcible, 
but  for  logical  treatment  it  needs  to  be  interpreted  in  the  general  form,' 


OF  TERMS   AND   THEIR   DENOTATION 


31 


M 


By  autonomasia  proper  names  may  become  general  terms,  as  if  we 
say  'A  Johnson'  would  not  have  written  such  a  book— i.e.,  any  man  of  his 
genius  for  elaborate  eloquence. 

A  Collective  term  denotes  a  multitude  of  similar  things,  not 
distributive^,  but  considered  as  forming  one  whole,  as  'regi- 
ment,' 'fiock,'  'nation.'  If  a  multitude  of  things  have  no 
resemblance,  except  the  fact  of  being  considered  as  parts 
of  one  whole,  as  'the  world,'  or  'the  town  of  Nottingham' 
(meaning  its  streets  and  houses,  open  spaces,  people,  and 
civic  organisation),  the  term  denoting  them  as  a  whole  is 
Singular;  but  'the  world'  or  'town  of  Nottingham,'  meaning 
the  inhabitants  only,  is  Collective. 

In  their  strictly  collective  use,  all  such  expressions  are 
equivalent  to  Singular  Terms;  but  many  of  them  may  also 
be  used  as  General  Terms,  as  when  we  speak  of  'so  many 
regiments  of  the  line,'  or  discuss  the  'plurality  of  worlds';  and 
in  this  general  use  they  denote  any  of  a  multitude  of  things  of 
the  same  kind— regiments,  or  habitable  worlds. 

Names  of  substances,  such  as  'gold,'  'air,'  'water,'  may 
be  employed  as  Singular,  Collective,  or  General  terms  ;  though, 
perhaps,  as  Singular  Terms  only  figuratively,  as  when  we  say 
Go/d  is  ki?ig.  if  we  say  with  Thales,  '  Water  is  the  source  of 
all  things;  'water'  seems  to  be  Collective.  But  substantive 
names  are  frequently  used  as  General  Terms.  For  example, 
Go/d  is  heavy  means  '  in  comparison  with  other  things,'  such 
as  water.  And,  plainly,  it  does  not  mean  that  the  aggregate 
of  gold  is  heavier  than  the  aggregate  of  water,  but  only  that  its 
specific  gravity  is  greater;  that  is,  bulk  for  bulk,  any  piece  of 
gold  is  heavier  than  water. 

Finally,  any  class-name  may  be  used  collectively  if  we  wish 
to  assert  something  of  the  things  denoted  by  it,  not  distri- 
butively  but  altogether,  as  that  Sheep  are  more  numerous  than 
ivolves. 


♦ 

I 


CHAPTER  IV 
THE   CONNOTATION   OF  TERMS 

§  I.  Terms  are  next  to  be  classified  according  to  their 
Connotation — that  is,  accf»rding  lo  what  they  imply  as 
characteristic  of  the  things  denoted.  We  have  seen  that 
general  names  are  used  to  denote  many  things  in  the  same 
sense,  because  the  things  denoted  resemble  one  another  in 
certain  ways :  it  is  this  resemblance  in  certain  points  that  leads 
us  to  class  the  things  together  and  call  them  by  the  same 
name ;  and  therefore  the  points  of  resemblance  constitute  the 
sense  or  meaning  of  the  name,  or  its  Connotation,  and  limit 
its  applicability  to  such  things  as  have  these  characteristic 
qualities.  '  Sheep,'  for  example,  is  used  in  the  same  sense, 
to  denote  any  of  a  multitude  of  animals  that  resemble  one 
another :  iheir  size,  shape,  woolly  coats,  cloven  hoofs,  innocent 
ways  and  edibility  are  well  known.  When  we  apply  to 
anything  the  term  '  sheep ',  we  imply  that  it  has  these  quali- 
ties :  '  sheep,'  denoting  the  animal,  connotes  its  possessing 
these  characteristics ;  and,  of  course,  it  cannot,  without  a 
figure  of  speech  or  a  blunder,  be  used  to  denote  anything  that 
does  not  possess  all  these  qualities.  It  is  by  a  figure  of  speech 
that  the  term  '  sheep '  is  applied  to  some  men ;  and  to  apply  it 
to  goats  would  be  a  blunder. 

All  general  names,  and  therefore  not  only  class-names,  like 
'  sheep,'  but  all  attributives,  have  some  connotation.  *  Woolly  ' 
denotes  anything  that  bears  wool,  and  connotes  the  fact  of 
bearing  wool ;  '  innocent '  denotes  anything  that  habitually 
does  no  harm  (or  has  not  been  guilty  of  a  particular  offence), 


THE   CONNOTATION   OF   TERMS  33 

and  connotes  a  harmless  character  (or  freedom  from  particular 
guilt);  'edible'  denotes  whatever  can  be  eaten  with  good 
results,  and  c^notes  its  suitability  for  mastication,  deglutition, 
digestion,  and  assimilation. 

§  2.  But  whether  all  terms  must  connote  as  well  as  denote 
something,  has  been  much  debated.  Proper  names,  according 
to  what  seems  the  better  opinion,  are,  in  their  ordinary  use,  not 
connotative.  To  say  that  they  have  no  meaning  may  seem 
violent :  if  any  one  is  called  Alphonso  Schultze  (a  name  which 
I  invent,  hoping  that  no  man  bears  it),  this  name  no  doubt 
means  a  great  deal  to  his  friends  and  neighbours,  reminding 
them  of  his  stature  and  physiognomy,  his  air  and  gait,  his  wit 
and  wisdom,  some  queer  stories,  and  an  indefinite  number  of 
other  things.  But  all  this  significance  is  local  or  accidental ; 
,it  only  exists  for  those  who  know  the  individual  or  have  heard 
him  described:  whereas  a  general  name  gives  information 
about  any  thing  or  person  it  denotes  to  everybody  who  under- 
stands the  language,  without  any  particular  knowledge  of  the 
individual. 

We  must  distinguish,  in  fact,  between  the  peculiar  associations  of  the 
proper  name  and  the  commonly  recognised  meaning  of  the  general 
name.  This  is  why  proper  names  are  not  in  the  dictionary.  Such  a 
name  as  London,  to  be  sure,  or  Napoleon  Buonaparte,  has  a  significance 
not  merely  local ;  still,  it  is  accidental.  '  London  '  suggests  very  diffe- 
rent things  to  a  Londoner,  to  his  country  cousin,  and  to  a  merchant  in 
Buenos  Ayres.  'Napoleon  Buonaparte"  excites  different  ideas  in 
France  and  in  Germany,  and  had  another  meaning  for  our  grandfathers 
than  it  has  for  us.  Moreover,  these  names  are  borne  by  other  places 
and  persons  than  those  that  have  rendered  them  famous.  There  are 
Londons  in  various  latitudes,  and,  no  doubt,  many  Napoleon  Buona- 
partes in  Louisiana  ;  and  each  name  has  in  its  several  denotations  an 
altogether  different  suggestiveness.  For  its  suggestiveness  is  in  each 
application  determined  by  the  peculiarities  of  the  place  or  person  denoted, 
and  had  any  other  name  been  given  it  would  have  gathered  much  the 
same  associations.  If  the  French  hero  had  gone  by  some  fiat  and 
vulgar  appellation,  it  would  have  impoverished  the  romance  of  history  ; 
but  the  great  bulk  of  its  significance  for  us  would  now  be  the  same. 

However,  the  scientific  grounds  of  the  doctrine  that  proper 
nfames  are  non-connotative,  are  these :  The  peculiarities  that 

c 


34        LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

distinguish  anln  dividual  person  or  thing  are  admitted  to  be 
infinite,  and  anything   less  than  a  complete  enumeration  of 
these  peculiarities  may  fail   to   distinguish   and   identify  the 
individual.     For,  short  of  a  complete  enumeration  of  them, 
the  description  may  be  satisfied  by  two  or  more  individuals; 
and  in  that  case  the  term  denoting  them,   if  limited  by  such 
a  description,  is  not  a  proper  but  a  general   name,  since  it  is 
applicable  to  two  or  more  in  the  same  sense.     The  existence 
of  other  individuals  to  whom  it  might  apply  may  be  highly 
improbable ;   but,  if  it  be  logically  possible,  that  is  enough. 
On  the  other  hand,  the  enumeration  of  infinite  peculiarities 
is   certainly   impossible.      Therefore   proper   names   have   no 
assignable  connotation.     The  only  escape  from  this  reasoning 
lies  in  falling  back  upon  time  and   place,  the   principles   of 
individuation,  as  constituting  the  connotation  of  proper  names. 
Two  things  cannot  be  at  the  same  time  in  the  same  place  : 
hence  '  the  man  who  was  at  a  certain  spot  on   the  bridge  of 
Lodi  at  a  certain  instant  in  a  certain  year,'  suffices  to  identify 
Napoleon  Buonaparte  for  that  instant.     Supposing  no  one  else 
to  have  borne  the  name,  then,  is  this  its^onnotation  ?    No  one, 
I  think,  has  ever  thought  or  said  so.  And  at  any  rate,  time 
and  place  are  only  extrinsic  determination^f^itable  indeed  to 
events  like  the  battle  of  Lodi,   or  to  ^ftaces  themselves  like 
London) ;    whereas   the   connotation  of  a  general   term,  like 
*  sheep,'   consists   of    intrinsic   qualities.      Hence,    then,    the 
scholastic  doctrine   'that  individuals  have  no   essence'   (see 
chap.  xxii.  §  9),  and  Hamilton's  dictum   '  that  every  concept 
is  inadequate  to  the  individual,'  are  justified. 

General  names,  when  used  as  proper  names,  lose  their 
connotation,  as  Euxine  or  Newfoundland. 

Singular  terms,  other  than  Proper,  have  connotation ;  either 
in  themselves,  like  the  singular  pronouns  *  he,'  *  she,'  it,'  which 
are  general  in  their  applicability,  though  singular  in  applica- 
tion ;  or,  derivatively,  from  the  general  names  that  combine  to 
form  them,  as  in  *  the  first  Emperor  of  the  French '  or  the 
'  Capital  of  the  British  Empire.' 


4 


THE  CONNOTATION   OF  TERMS  35 

§  3-  Whether  Abstract  Terms  have  any  connotation  is 
another  disputed  question.  We  have  seen  that  they  denote  a 
quahty  or  quah'ties  of  something,  and  that  is  precisely  what 
general  terms  connote  :  '  honesty  '  denotes  a  quality  of  some 
men;  'honest'  connotes  the  same  quality,  whilst  denoting  the 
men  who  have  it. 

The  denotation  of  abstract  terms  thus  seems  to  exhaust  their  force  or 

Z^Z.fu;  It  ?"  P':°P°^«<^'  however,  to  regard  them  as  connoting 
the  qualities  they  directly  stand  for,  and  not  denoting  anything  •  but 

T:11  "  T  "°'r  ■  ""^  "'""''  ^°'"^«""«  -^  "'^  same'thini  as  to 
be  the  name  of  something  (whether  real  or  unreal),  which  every  term 
must  be.     It  IS  a  better  proposal  to  regard  their  denotation  and  conn^- 

m  a°n"s  ^toT/l     f '  '^°".g^°P«"   '°  '"«  objection   that  'connote' 

means     to  mark  along   with '   something  else,   and   this  plan   leaves 

nothing  else.     Mill  thought  that  abstract  terms  are  connotative  whin 

besides  denoting  a  quality,  they  suggest  a  quality  of  that  quality  (as 

fault    implies  ■  hurtfulness ' ;  but  against  this  it  may  be  urged  that  one 

quality  cannot  bear  another,  since  every  qualiHcation  of  a  quality  con! 

titutes  a  distinct  quality  in  the  total  (■  millc-whi.eness  ■  is  distinct  from 

whiteness,'  c/.  chap.  iii.  §  4).    After  all.  if  it  is  the  most  consis  en" 

nltatio^f  ""'  '''''  "'^'  ^'''"■'"'  "''"  P™P"^'  '^™=  ^^^  "o  ^on- 

Bitt  if  abstract  terms  must  be  made  to  connote  something 
should  It  not  be  those  things,  indefinitely  suggested,  to  which 
the  qualities  belong.?  Thus,  'whiteness'  may  be  supposed  to 
connote  either  snow  or  vapour,  or  any  white  thing,  apart  from 
one  or  other  of  which  the  quality  has  no  existence ;  whose 
existence  therefore  it  implies.  By  this  course  the  denotation 
and  connotation  of  abstract  and  of  general  names  would  be 
exactly  reversed.  But  the  whole  difficulty  may  be  avoided  by 
makmg  it  a  rule  to  translate,  for  logical  purposes,  all  abstract 
mto  the  corresponding  general  terms. 

§  4-  If  we  ask  how  the  connotation  of  a  term  is  to  be 
known,  here  again  the  answer  depends  upon  the  way  it  is  used 
If  used  scientifically,  its  connotation  is  determined  by,  and  is 
the  same  as,  its  definition ;  and  the  definition  is  determined 
by  examming  the  things  to  be  denoted,  as  we  shall  see  in 
chap.  xxii.     If  the  same  word  is  used  as  a  term  in  different 


36       LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

sciences,  as  'property'  in  Law  and  in  Logic  it  will  be  dif- 
ferently defined  by  them,  and  will  have,  in  each  use,  a  corres- 
nondindy  different  connotation.  But  terms  used  m  popular 
discourse  should,  as  far  as  possible,  have  their  connotations 
determined  by  classical  usage,  i.e.,  by  the  sense  in  which  they 
are  used  by  writers  and  speakers  who  are  acknowledged  masters 
of  the  language,  such  as  Dryden  and  Burke.  In  this  case  the 
classical  connotation  determines  the  definition  ;  so  that  to 
define  terms  thus  used  is  nothing  else  than  to  analyse  their 

accepted  meanings. 

It  must  not,  however,  be  supposed  that  in  popular  use  the 
connotation  of  any  word  is  invariab'e.  Logicians  have  at- 
tempted to  classify  terms  into  Univocal  (having  only  one 
meaning)  and  ^:quivocal  (or  ambiguous) ;  and  no  doubt  some 
words  (like  civil,  natural,  proud,  liberal,  humorous),  are  more 
manifestly  liable  to  ambiguous  use  than  some  others.  But  m 
truth  all  general  terms  are  popularly  and  classically  used  in 
different  senses. 

Figurative  or  tropical  language  chiefly  consists  in  the  transfer  of 
Hguratue  or  I     ^^^^  ,      „.j„uor  or  metonymy.     In  the  course  of 

words  to  new  ^^'X^ZLT^^ks-^nA  before  the  time  of  Dryden 
years  too.  words  c^hangethe^rmeanmg^^^^  ^^  ^^^^  .^  ^^ 

Z:t^:oLTt:i'::ZTZ  Bacon,  MiUon.  and.Sir  Thomas  Browne 
since  become.  j=  some  tense  they  originally 

haTin  lltif^ough  in  En  U^h  they  had  ..^.^^  another  meaning. 
Spenser  and'  Shakespeare,  besides  this  practiceysometimes  use  words 
fn  a  way  that  can  only  be  justified  by  their  choosing  to  have  it  so.  St.U. 
in  a  way  «at  ca         y  variation  in  the  sense  of  words. 

Tr^lr  ^ch  '^^tZ:^  to  denote  are  often  so  complicated  or 
T  aZ   he  assemblac^e  interfusion,  or  gradation  of  their  qualities  . 

tZo.  the  tMn^  ^: --  -  ^-' ™^I  -~-4 

Cy  t.'.  and  the  only  escape  fro.  it   short  ^^^^^  -rv^wt 

?    t  or  to  The  resources  of  the  literary  art,  to  convey  the  true  meaning. 
oT^;Cstinruateadecep^  Against  this  evil  the  having 

bee'n  boTn  Ice  Dryden  is  no  protection.      It    behoves  us.  then,  to 


THE   CONNOTATION   OF  TERMS 


37 


remember  that  terms  are  not  classifiable  into  Univocal  and  /Equivocal, 
but  that  all  terms  are  susceptible  of  being  used  aequivocally.  and  that 
honesty  and  lucidity  require  us  to  try,  as  well  as  we  can,  to  use  each 
term  univocally  in  the  same  context. 

The  context  of  any  proposition  always  proceeds  upon  some 
assumption  or  understanding  as  to  the  scope  of  the  discussion? 
which  controls  the  interpretation  of  every  statement  and  of 
every  word.  This  has  been  called  the  "  universe  of  discourse": 
an  older  name  for  it,  revived  by  Dr.  Venn,  and  surely  a  better 
one,  is  siippositio.  If  now  we  are  talking  of  children,  and  'play' 
is  mentioned,  the  suppositio  limits  the  suggestiveness  of  the 
word  in  one  way ;  whilst  if  Monaco  is  the  subject  of  conversa- 
tion, the  same  word  '  play,'  under  the  influence  of  a  different 
supposition  excites  altogether  different  ideas.  Hence  to  ignore 
the  suppositio  is  a  great  source  of  fallacies  of  equivocation- 
*  Man  '  is  generally  defined  as  a  kind  of  animal ;  but  '  animal ' 
is  often  used  as  opposed  to  and  excluding  man.  *  Liberal '  has 
one  meaning  under  the  suppositio  of  politics,  another  with 
regard  to  culture,  and  still  another  as  to  the  disposal  of  one's 
private  means.  Clearly,  therefore,  the  connotation  of  general 
terms  is  relative  to  the  suppositio^  or  "universe  of  dis- 
course." 

§  5.  Relative  and  Absolute  Terms. — Some  words  go  in 
couples  or  groups  :  like  '  up-down,'  '  former-latter,'  '  father- 
mother-children,'  '  hunter-prey,'  *  cause-effect,'  etc.  These  are 
called  Relative  Terms,  and  their  nature,  as  explained  by  Mill, 
is  that  the  connotations  of  the  members  of  such  a  pair  or  group 
are  derived  from  the  same  set  of  facts  (the  fundament um  re- 
lationis).  There  cannot  be  an  '  up '  without  a  '  down,'  a  'father' 
without  a  '  mother '  and  '  child  ' ;  there  cannot  be  a  '  hunter ' 
without  something  hunted,  nor  '  prey '  without  a  pursuer. 
What  makes  a  man  a  '  hunter '  is  his  activities  in  pursuit ;  and 
what  turns  a  chamois  into  '  prey '  is  its  interest  in  these 
activities.  The  meaning  of  both  terms,  therefore,  is  derived 
from  the  same  set  of  facts  \  neither  term  can  be  explained 
without  exDlaining  the  other,  and  neither  can  with  propriety  be 


38        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

used  without  reference  to  the  other,  or  to  some  equivalent,  as 

*  game '  for  *  prey.' 

In  contrast  with    such  Relative  Terms,  others  have  been 
called  Absolute  or  Non-relative.     Whijst  '  hunter '  and  *  prey  ' 
are  relative,  '  man '  and  '  chamois '  have  been  considered  abso- 
lute, as  there  may  be  no  special  connection  between  their 
meanings.     However,  if  we  believe  in  the  unity  of  Nature  and 
in    the   relativity  of  knowledge   (that   is,   that  all  knowledge 
depends  upon  comparison,  or  a  perception  of  the  resemblances 
and  differences  of  things),  it  follows  that  nothing  can  be  com- 
pletely understood  except  through  its  agreements  or  contrasts 
with  everything  else,  and  that  all  terms  derive  their  connotation 
from  the  same  set  of  facts,  namely,  from  general  experience. 
Thus  both  man  and  chamois  are  animals ;   this  fact  is  an  im- 
portant part  of  the  meaning  of  both  terms,  and  to  that  extent 
they  are  relative  terms      '  Five  yards '  and  '  five  minutes  '  are 
very  different   notions,  yet   they  are  profoundly  related;    for 
their  very  difference  helps  to  make  both  notions  distinct ;  and 
their  intimate  connection  is  shown  in  this,  that  five  yards  are 
traversed  in  a  certain  time,  and  that  five  minutes  are  measured 
by  the  motion  of  an  index  over  some  fraction  of  a  yard  upon 

the  dial. 

The   distinction,    then,    between    relative   and    non-relative 
terms  must  rest  not  upon  a  fundamental  difference  between 
them   (since,   in  fact,    all   words  are    relative)   but  upon  the 
way   in    which   words   are   used.     We   have   seen  that  some 
words,    such     as    'up-down,'    'cause-effect,'    can     only     be 
used  relatively;   and  these  might,  for  distinction,  be  called 
Correlatives.      But    other   words,    whose   meanings   are   only 
partially  interdependent,  may  often  be  used  without  attending 
to  their  relativity,  and  may  then  be  considered  as  Absolute. 
We  cannot  say  '  the  hunter  returned  empty  handed,'  without 
implying  that  '  the  prey  escaped ' ;  but  we  may  say  '  the  man 
went  supperless  to  bed,'  without  implying  that  '  the  chamois  re- 
joiced upon  the  mountain.'  Such  words  as  '  man  '  and  ^chamois' 
may,  then,  in  their  use,  be,  as  to  one  another,  non-relative. 


i 


THE   CONNOTATION   OF  TERMS 


39 


To  illustrate  further  the  relativity  of  terms,  we  may  mention  some  of 
the  chief  classes  of  them. 

Numerical  order:  ist,  2nd,  3rd,  etc.  Note  that  ist  implies  2nd,  and 
2nd  ist ;  and  that  3rd  implies  ist  and  2nd,  but  these  do  not  imply  3rd; 
and  so  on. 

Order  in   Time,  or  Place:    early-punctual-late;   right-middle-left; 

North-South,  etc. 

As  to  Extent,  Volume  and  Degree :  greater-equal-less ;  large- 
medium-small  ;  whole  and  part. 

Genus  and  Species  {cf.  chaps,  xxi.-ii.-iii.).  Sometimes  a  term  con- 
notes all  the  attributes  that  another  does,  and  more  besides,  which, 
as  distinguishing  it,  are  called  differential.  Thus  'man'  connotes  all 
that  'animal '  does,  and  also  (as  differenticB)  the  erect  attitude,  articulate 
speech,  and  other  attributes.  In  such  a  case  as  this,  where  we  have 
well-marked  natural  classes,  the  term  whose  connotation  is  included  in 
the  others'  is  called  a  Genus  of  that  Species.  Thus  we  have  a  Genus, 
triangle  ;  and  a  Species,  isosceles,  marked  off  from  all  other  triangles  by 
the  differential  quality  of  having  two  equal  sides.  Or,  again :  Genus,  book ; 
Species,  quarto;  Difference,  having  each  sheet  folded  into  four  leaves. 

There  are  other  cases  where  these  expressions, '  genus '  and  '  species,' 
cannot  be  so  applied  without  a  departure  from  usage,  as,  e.g.,  if  we 
call  snow  a  species  of  the  genus  '  white  '  (for  '  white '  is  not  a  recog- 
nised class),  although  the  connotation  of  white  {i.e.,  whiteness)  is  part 
of  the  connotation  of  snow,  just  as  the  qualities  of  '  animal '  are  amongst 
those  of  '  man. '  For  logical  purposes,  however,  it  seems  desirable  to 
use  '  genus  and  species '  to  express  that  relativity  of  terms  which 
consists  in  the  connotation  of  one  being  part  of  the  connotation  of  the 
other. 

Two  Terms  whose  connotations  include  that  of  a  third,  whilst  at  the 
same  time  exceeding  it,  are  (in  relation  to  that  third  term)  called  Co- 
ordinate. Thus  in  relation  to  '  white,'  snow  and  silver  are  co-ordinate ; 
in  relation  to  colour,  yellow  and  red  are  co-ordinate.  And  when  all 
three  terms  stand  for  recognised  natural  classes,  the  co-ordinate  terms 
are  called  co-ordinate  species  ;  thus  man  and  chamois  are  (in  Logic)  co- 
ordinate species  of  the  genus  animal. 

§  6.  From  such  examples  of  terms  related  as  whole  and 
part  in  connotation,  it  is  easy  to  see  the  general  truth  of  the 
doctrine  that  as  connotation  decreases,  denotation  increases :  for 
'  animal,'  with  less  connotation  than  man  or  chamois,  denotes 
many  more  objects;  'white,'  with  less  connotation  than  snow 
or  silver  denotes  many  more  things.  It  is  not,  however,  certain 
that  this  doctrine  is  always  true  in  the  concrete :  as  there  may  be 
a  term  connoting  two  or  more  qualities,  all  of  which  qualities 


40       LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

are  peculiar  to  all  the  things  it  denotes  ;   and,  if  so,  by  sub- 
tracting one  of  the  qualities  from  its  connotation,  we  should 
not  increase  its  denotation.     If  '  man,'  for  example,  has  among 
mammals  the  two  peculiar  attributes  of  erectness  and  articu- 
late speech,  then,  by  omitting  'articulate    speech'  from  the 
connotation  of  man,  we  could  not  use  the  name  of  any  more 
of  the  existing  mammalia  than  we  can  at  present.     Still  we 
might   have  been  able  to  do  so ;   there  might  have  been  an 
erect  inarticulate  ape,  and  perhaps  there  once  was  one ;   and, 
if  so,  to  omit  'articulate'  from  the  connotation  of  man  would 
make  the  term  '  man  '  denote  that  animal  (supposing  that  there 
was  no  other  difference  to  exclude  it).     Hence,  potentially,  an 
mcrease  of  the  connotation  of  any  term  implies  a  decrease  of 
its  denotation.     And,  on  the  other  hand,  we  can  only  increase 
the  denotation  of  a  term,  or  apply  it  to  more  objects,  by  de- 
creasing its  connotation ;  for  if  the  new  things  denoted  by  the 
term  had  already  possessed  its  whole  connotation  they  must 
already  have  been  denoted  by  it.     However,  we  may  increase 
the  knoivn  denotation  without  decreasing  the  connotation,  if  we 
can  discover  the  full  connotation  in  things  not  formerly  sup- 
posed to  have  it;   or  if  we  can  impose  the  requisite  qualities 
upon  new  individuals,  as  when  by  annexing  some  millions  of 
Africans  we  extend  the  denotation  of  '  British  subject '  without 
altering  its  connotation. 

Many  of  the  things  noticed  in  this  chapter,  especially  in  this  section 
and  the  preceding,  will  be  discussed  at  greater  length  in  the  chapters  on 
Classification  and  Definition. 

§  7-  Contradictory  Relatives.— Every  term  has,  or  may  have, 
another  corresponding  with  it  in  such  a  way  that  whatever 
differential  qualities  (§5)  it  connotes,  this  other  connotes 
merely  their  absence;  so  that  one  or  the  other  is  alwaxs 
formally  predicable  of  any  Subject,  but  both  these  terms  are 
never  predicable  of  the  ^anie  Subject  in  the  same  relation  : 
such  pairs  of  terms  ar(L>^d  Contradictories.  Whatever 
Subject  we  take,  it  is  either  ^ible  or  invisible,  but  not  both; 
either  human  or  non-human,  but  not  both. 

(A  >x  ^ 


Ai' 


THE   CONNOTATION   OF  TERMS  41 

ourselves  trifled  uith   if  any  one  told  us  that  'A  mountain  is  either 

anTrtUr'r"'!'"'"",'  '^°*-'    ''  '^  ^^-''°'-  terms  sh'fx 
subject  white  e/sTrt  "f    '°  ''  -"'-Victories  in  relation  to  any 

flourish  a  dumb  hl'll^f     !  u        P^^e^-^-as  if  we  ask  whether  to 

or  impeccabmt^^te  h  ""^^''  °'  '°  ''"''"  *^  '"'"^  ^^  '"'""i™. 

visibTe'^reMlr  ,n  ^h  ""^  r"-""-"""-     S™"^^'^-  "^'"le  and  ]„: 

hold  upon  a  sound  or  TiT'  °  ""'^'=""*^  "^''''  ^°  '^^^  '^^^  ^ave  no 
«cation^s  as  •  t^h IbJ  ^^^l^  t^  : -traTiel:^-  ^^  ^""  -^"- 

Again,  the  above  definition  of  Contradictories  tells  us  that 

relation        that  .s,  at  the  same  time  or  place,  or  under  the 
same  condu.ons.     The  lamp  is  visible  to  me  now,  but  wH 

b  tT      ,'      •    '""   '  °"''-   ""  '"'  °f  '^  -  "-  visible, 
but  the  other  ,s  not :  therefore,  without  this  restriction,  "  i, 

the  same  relat.on,"  few  or  no  terms  would  be  contradictory, 
actiln  -T  d  ?"'f  '"'"■  "  """'  '"«^"  •  °"  'he  whole  '  or  •  in  a  certain 

that  seem  contradictor^are  prldi  abroHh"'  '  '''\^"">T'y'  '--= 
the  same  relation."  In  order  to  avo^thl  ^^"'  '"u^'"' '''"  "°'  " '" 
only  to  construct  the  tLm7„       f  ambiguity,  however,  we  have 

whole  ■    7nT.K  .  ^^  '°  '"'P'""'''  "^«  relation,  as  ■  wise  on  the 

the^thde  sti^rTv  aT''  '""''"  "'  contradictory  •  nofw^L  on 
another  not  btck  hii;  •  IrtheTfif  u"  ""^^  ""'''  ""^^"^  ''-"■  -' 
stating  the  age  reftrred  to  """""  "  "'"^^"'^^"^  ^^'"''-ble  by 

dicto";  terrrdTfficull""'-"'  '  V^'  ''"^^""^  ■"  *«  "-  °f  -ntra- 
of  nZX^enot^TTZ'      "  "'^ -"«-«- change  or  .flux' 

ratdrf5-"— 

JCL.L,  ai  least  as  last  as  we  can  ntfpr  fV.orv,  .  r^    -r 

black,  since  (like  everything  elsJ)  his  haTr  L  I  "'  '"' -^  """''  ""^'^  '' 
not  black  though  ft  J}..        TJ  ^  changing,  it  must  now  be 

liUL  uiacK,  tnough  (to  be  sure)  it  may  still  seem  hlart      ti,^  ^-m     i 

the  terms  of  human  discourse  assume  a  certain  fixity  of  things    ^Ce" 
thing  at  every  moment  changes    but  for  th^  rr^^o.         .   ^""^gs.  every- 
perceive  this  change  nor  expS  it  P-t  we  can  neither 


^ 


42        LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

This  paradox,  however,  may,  I  suppose,  be  easily  overstated.  The 
change  that  continually  goes  on  in  nature  consists  in  the  movements  of 
masses  or  molecules,  and  such  movements  of  things  are  compatible 
with  a  considerable  persistence  of  their  qualities.  Not  only  are  the 
molecular  changes  always  going  on  in  a  piece  of  gold  compatible  with 
its  remaining  yellow,  but  its  persistent  yellowness  depends  on  the  con- 
tinuance of  some  of  those  changes.  And  as  much  may  be  said  for  the 
blackness  of  a  man's  hair,  though,  no  doubt,  at  a  certain  age  its  colour 
may  begin  to  be  problematical,  and  the  applicability  to  it  of  '  black  '  or 
'  not-black  '  may  become  a  matter  of  genuine  anxiety.  Whilst  being  on 
our  guard,  then,  against  fallacies  of  contradiction  arising  from  the  im- 
perfect correspondence  of  fact  with  thought  and  language,  we  shall 
often  have  to  put  up  with  it.  Candour  and  humility  being  satisfied 
with  the  above  acknowledgment  of  the  subtlety  of  nature,  this  book  will 
henceforward  proceed  upon  the  postulate— that  it  is  possible  to  use 
contradictory  terms  such  as  cannot  both  be  predicated  of  the  same 
subject  in  the  same  relation,  though  one  of  them  may  be;  that,  for 
example,  it  may  be  truly  said  of  a  man  for  some  years  that  his  hair  is 
black  ;  and,  if  so,  that  during  those  years  to  call  it  not-black  is  false  or 
extremely  misleading. 

It  must  be  observed  that  the  most  opposed  terms  of  the 
literary  vocabulary,  such  as  'wise-foolish,'  old-young,'  'sweet- 
bitter,'  are  rarely  true  contradictories  :  wise  and  foolish,  indeed, 
cannot  be  predicated  of  the  same  man  in  the  same  relation ; 
but  there  are  many  middling  men,  of  whom  neither  can  be 
predicated  on  the  whole.  For  the  comparison  of  quantities, 
again,  we  have  three  correlative  terms,  greater,  equal,  less,  and 
none  of  these  is  the  contradictory  of  either  of  the  others.  In 
fact,  the  contradictory  of  any  term  is  one  that  denotes  the  sum 
of  its  co-ordinates  (§  6) ;  and  to  obtain  a  contradictory,  the 
surest  way  is  to  coin  one  by  prefixing  to  the  given  term  the 
particle  'not'  or  (sometimes)  'non':  as  'wise-not-wise,'  'human- 
non-human,'  '  greater-not-greater.' 

The  separate  word  '  not '  is  surer  to  constitute  a  contradictory  than 
the  usual  prefixes  of  negation,  '  un- '  or  'in-',  or  even  'non.'  Since 
compounds  of  these  are  generally  warped  by  common  use  from  a  purely 
negative  meaning.  Thus,  '  Nonconformist '  does  not  denote  everybody 
who  fails  to  conform.  'Unwise'  is  not  equivalent  to  'not-wise,'  but 
means  '  rather  foolish  ' ;  a  very  foolish  action  is  not-wise,  but  can  only 
be  called  unwise  by  meiosis  or  irony.     Still,  negatives  formed  by  '  in  ' 


"< 


i 

I- 


THE   CONNOTATION   OF  TERMS  43 

or  •  un  '  or  '  non  '  are  sometimes  really  contradictory  of  their  positives  • 
as 'visible-m visible,'  'equal-unequal.' 

§  8.  The  distinction  between  Positive  and  Negative  terms  is  not  of 
much  value  in  Logic,  what  importance  would  else  attach  to  it  being 
absorbed  by  the  more  definite  distinction  of  contradictories.  For  con- 
tradictories are  positive  and  negative  in  essence  and.  when  least  am- 
biguously stated,  also  in  form.  And.  on  the  other  hand,  as  we  have 
seen,  when  positive  and  negative  terms  are  not  contradictory,  they  are 
misleading.  As  with  'wise-unwise,'  so  with  many  others,  such  as 
•  happy-unhappy ;  '  which  are  not  contradictories  ;  since  a  man  may  be 
neither  happy  nor  exactly  unhappy,  but  indifferent,  or  (again)  so  miser- 
able that  he  can  only  be  called  unhappy  by  a  figure  of  speech.  In  fact 
in  the  common  vocabulary  a  formal  negative  often  has  a  limited  posi- 
tive sense ;  and  this  is  the  case  with  unhappy,  signifying  the  state  of 
teeling  in  the  milder  shades  of  purgatory. 

But  when  a  Negative  term  is  fully  contradictory  of  its 
Positive,  it  is  said  to  be  Infinite;  because  it  denotes  an 
unascertained  multitude  of  things,  a  multitude  only  limited 
by  the  Positive  term  and  the  siippositio  ;  thus  '  not-wise '  denotes 
all,  except  the  wise,  within  the  suppositio  of '  intelligent  beings.' 
Indeed,  formally  (disregarding  any  suppositio),  such  a  Negative 
Term  stands  for  all  possible  terms  except  its  Positive:  x 
denotes  everything  but  X ;  and  '  not-wise '  may  be  taken  to 
include  stones,  triangles  and  hippogriffs.  In  this  sense,  every 
Negative  term  has  some  positive  meaning,  though  a  very  in- 
definite one,  not  a  specific  positive  force  like  'unwise'  or 
'  unhappy.'  It  denotes  any  and  everything  that  has  not  the 
attributes  connoted  by  the  corresponding  Positive  Term. 

Privative  Terms  connote  the  absence  of  a  quality  that  normally 
belongs  to  the  thing  denoted,  as  '  blind  '  or  '  deaf.'  We  may  predicate 
•  blind '  or  '  deaf  of  a  man,  dog  or  cow  that  happens  not  to  be  able  to 
see  or  hear,  because  the  powers  of  seeing  and  hearing  generally  belong 
to  these  species  ;  but  of  a  stone  or  idol  these  terms  can  only  be  used 
figuratively.  Indeed,  since  the  contradictory  of  a  privative  carries  with 
It  the  privative  limitation,  a  stone  is  strictly  '  not-blind  '  ;  that  is,  it  is 
'  not-something-that-normally-having-sight-wants-it.' 

Contrary  Terms  are  those  that  severally  connote  the  absence 
of  differential  qualities  possessed  by  the  others,  and  therefore 
cannot  be  predicated  of  the  same  Subject  in  the  same  relation  : 


^ 


ps^l 


44 


LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


and,  so  far,  they  resemble  Contradictory  Terms,  but  differ 
from  them  in  this,  that  each  of  them  connotes  some  positive 
differential  quality  which  limits  it  to  part  of  the  denotation 
excluded  by  the  others;  so  that,  possibly,  neither  of  two 
contraries  is  truly  predicable  of  a  given  subject.  Thus  '  blue ' 
and  'red'  are  Contraries,  for  they  cannot  both  be  predicated  of 
the  same  thing  in  the  same  relation  ;  but  are  not  Contradictories, 
since,  in  a  given  case,  neither  may  be  predicable :  if  a  flower  is 
blue  in  a  certain  part,  it  cannot  in  the  same  part  be  red ;  but 
it  may  be  neither  blue  nor  red,  but  yellow  ;  though  it  is  certainly 
either  blue  or  not-blue.  All  Co-ordinate  terms  are  formal 
Contraries ;  but  if,  in  fact,  a  series  of  Co-ordinates  comprises 
only  two  (as  male-female),  they  are  Contradictories;  since 
each  includes  all  that  area  of  the  suppositio  which  the 
other  excludes. 

The  extremes  of  a  series  of  co-ordinate  terms  are  Opposites ;  as,  in  a 
list  of  colours,  white  and  black,  the  most  strongly  contrasted,  are  said 
to  be  opposites ;  or  as,  among  moods  of  feeling,  rapture  and  misery  are 
opposites.  But  this  distinction  is  of  slight  logical  importance.  Imper- 
fect Positive  and  Negative  couples,  like  '  happy  and  unhappy,'  which 
(as  we  have  seen)  are  not  contradictories,  are  often  called  opposites. 

The  members  of  any  series  of  Contraries  are  all  included  by 
any  one  of  them  and  its  contradictory,  as  all  colours  come 
under  '  red '  and  '  not-red,'  all  moods  of  feeling  under  '  happy 
and  not-happy.' 


^ 


CHAPTER  V 

THE   CLASSIFICATION   OF  PROPOSITIONS 

§  I.  It  is  usual  in  Logic  to  classify  Propositions  according 
to  Quantity,  Quality,  Relation  and  Modality. 

As  to  Quantity,  propositions  are  either  Universal  or  Par- 
ticular; that  is  to  say,  the  predicate  is  affirmed  or  denied 
either  of  the  whole  Subject  or  of  a  part  of  it— of  All  or  of 
Some  S. 

All  S  IS  P  (that  is,  P  is  predicated  of  all  S). 
Sojne  S  is  P  (that  is,  P  is  predicated  of  some  S). 

An  Universal  proposition  may  have  for  its  subject  a  Singular 
term,  a  Collective,  a  General  term  distributed,  or  an  Abstract 
term. 

(i)  A  Proposition  having  a  Singular  term  for  its  subject,  as  The  Queen 
is  gone  to  France,  is  called  a  Singular  Proposition ;  and  some  logicians 
regard  this  as  a  third  species  of  proposition  with  respect  to  quantity, 
distinct  from  the  Universal  and  the  Particular ;  but  this  is  needless. 

(2)  A  Collective  term  may  be  the  subject,  as  The  Black  Watch  is 
ordeved  to  India.  In  this  case,  as  well  as  in  singular  propositions,  a  pre- 
dication is  made  concerning  the  whole  subject  as  a  whole. 

(3)  The  subject  may  be  a  General  term  taken  in  its  full  denotation,  as 
A II  apes  are  sagacious ;  and  in  this  case  a  predication  is  made  concerning 
the  whole  subject  distributively  ;  that  is,  of  each  and  every  thing  that 
the  subject  stands  for. 

(4)  Propositions  whose  subjects  are  Abstract  terms,  though  they  may 
seem  to  be  formally  Singular,  are  really  as  to  their  meaning  distributive 
Universals  ;  since  whatever  is  true  of  a  quality  is  true  of  whatever  thing 
has  that  quality  so  far  as  that  quality  is  concerned.  Truth  will  prevail 
means  that  All  true  propositions  are  accepted  at  last  (by  sheer  force  of 
being  true,  in  spite  of  interests,  prejudices,  ignorance  and  indifference). 
To  bear  this  in  mind  may  make  one  cautious  in  the  use  of  abstract  terms. 


i» 


46        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

In  the  above  paragraphs  a  distinction  is  implied  between  Singular 
and  Distributive  Universals  ;  but  it  is  very  important  to  remember 
that,  technically,  every  term,  whether  Subject  or  Predicate,  when  taken 
in  its  full  denotation  (or  universally),  is  said  to  be  '  distributed,'  although 
this  word,  in  its  ordinary  sense,  would  be  directly  applicable  only  to 
General  terms.  In  the  above  examples,  then,  '  Queen,"  '  Black  Watch,' 
•apes,'  and  '  truth'  are  all  distributed  terms.  Indeed,  a  simple  defini- 
tion of  the  Universal  Proposition  is  '  one  whose  subject  is  distributed.' 

A  Particular  Proposition  is  one  that  has  a  general  term 
for  its  subject,  whilst  its  predicate  is  not  affirmed  or  denied 
of  everything  the  subject  denotes ;  in  other  words,  it  is  one 
whose  subject  is  not  distributed  :  as  Some  lions  inhabit  Africa. 

In  ordinary  discourse  it  is  not  always  explicitly  stated  whether  the 
predication  is  universal  or  particular ;  it  would  be  very  natural  to  say 
Liom  inhabit  Africa,  leaving  it,  as  far  as  the  words  go,  uncertain  whether 
we  mean  all  or  some  lions.     Propositions  whose  quantity  is  thus  left 
indefinite   are   technically   called  '  preindesignate,'  their  quantity  not 
being  stated  or  designated  by  any  introductory  expression  ;  whilst  pro- 
positions whose  quantity  is  expressed,  2iS  All  Foundling-hosjl^itals  have  a 
high  death-rate,  or  Some  nine  is  made  from  grapes,  are  said  to  be  predesig- 
nate.     Now,  the  rule  is  that  preindesignate  propositions  are,  for  logical 
purposes,  to  be  treated  as  particular;  since  it  is  an  obvious  precaution 
of  the  science  of  proof,  in  any  practical  application,  not  to  go  beyond  the 
evidence.     Still,  the  rule  may  be  relaxed  if  the  universal  quantity  of  a 
preindesignate  proposition  is  well  known  or  admitted,  as  in  Planets  shine 
with  reflected  light,  or  Sinners  are  wretched;  though,  indeed,  the  former  of 
these   examples,    I   suppose,    may   not   be   true   under  all   conditions. 
Again,  such  a  proposition  as  Man  is  the  paragon  of  animals  is  not  a  pre- 
indesignate, but  an  abstract  proposition  ;  the  subject  being  elliptical  for 
Man  according  to  his  proper  nature ;  and  the  translation  of  it  into  a  General 
proposition  is  not  All  men  are  paragons;  nor  can  Some  men  be  sufficient, 
since  an  abstract  can  only  be  adequately  rendered  by  a  distributed  term  ; 
bnt  we  must  say  All  men  who  approach  the  ideal. 

The  marks  or  predesignations  of  Quantity  commonly  used  in  Logic 
are:  for  Universals,  All,  Any,  Every,  Whatever  (in  the  negative  No  or 
No  one,  see  next  §)  ;  for  Particulars,  Some. 

It  should  be  carefully  noted  that  Some,  technically  used,  does  not 
mean  Some  only,  but  Some  at  least  (it  may  be  one,  or  more,  or  all).  If  it 
meant  '  some  only,'  every  particular  proposition  would  be  an  exclusive 
exponible  (chap.  ii.  §  3) ;  since  Only  some  men  are  wis»  implies  that  Some, 
men  are  not  wise.  Besides,  it  may  often  happen  in  an  investigation  that 
all  the  instances  we  have  observed  come  under  a  certain  rule,  though 


i 


f 


r 


f 


I    \ 


THE   CLASSIFICATION!   OF    PROPOSITIONS     47 

we  do  not  yet  feel  justified  in  regarding  the  rule  as  universal ;  and  this 
situation  is  exactly  met  by  the  expression  Some  (it  may  be  all). 

The  words  Many,  Most,  Few  are  generally  interpreted  to  mean  Some  ; 
but  as  Most  signifies  that  exceptions  are  known,  and  Few  that  the  excep- 
tions are  the  more  numerous,  propositions  thus  predesignate  are  in  fact 
exponibles,  amounting  to  Some  are  and  Some  arc  not.  If  to  work  with 
both  forms  is  too  cumbrous,  so  that  we  must  choose  one,  apparently 
Feiv  are  should  be  treated  as  Some  are  not.  The  scientific  course  to  adopt 
with  propositions  predesignate  by  Most  or  Few,  is  to  collect  statistics 
and  determine  the  percentage ;  thus,  Few  men  are  wise — say  2^  per  cent. 

The  Quantity  of  a  Proposition,  then,  is  usually  determined 
entirely  by  the  Quantity  of  the  subject,  whether  all  or  soj?te. 
Still,  the  quantity  of  the  predicate  is  often  an  important 
consideration ;  and  though  in  ordinary  usage  the  predicate 
is  never  predesignate,  Logicians  agree  that  in  every  Negative 
Proposition  (see  §  2)  the  predicate  is  'distributed,'  that  is  to 
say,  is  denied  altogether  of  the  subject,  and  that  this  is  in- 
volved in  the  form  of  denial.  To  say  So??ie  men  are  not  brave., 
is  to  declare  that  the  quality  for  which  men  may  be  called 
brave  is  not  at  all  found  in  the  Some  men  referred  to  :  and, 
similarly,  to  say  No  men  are  proof  agai?ist  flattery.,  cuts  off  the 
being  '  proof  against  flattery '  entirely  from  the  list  of  human 
attributes.  On  the  other  hand,  every  Affirmative  Proposition 
is  regarded  as  having  an  undistributed  predicate;  that  is  to 
say,  its  predicate  is  not  affirmed  exclusively  of  the  subject. 
Some  men  are  wise  does  not  mean  that  '  wise '  cannot  be 
predicated  of  any  other  beings ;  it  is  equivalent  to  Some 
men  are  wise  (7vhoever  else  may  be).  And  All  elephants  are 
sagacious  does  not  limit  sagacity  to  elephants :  regarding 
'  sagacious  '  as  possibly  denoting  many  animals  of  many  species 
that  exhibit  the  quality,  this  proposition  is  equivalent  to  '  All 
elephants  are  some  sagacious  animals.'  Clearly,  the  affirmative 
predication  of  a  quality  does  not  imply  exclusive  possession  of 
it  as  denial  implies  its  complete  absence;  and,  therefore,  to 
regard  the  predicate  of  an  affirmative  proposition  as  distributed 
would  be  to  go  beyond  the  evidence  and  to  take  for  granted 
what  had  never  been  alleged. 


48       LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

Some   Logicians,    seeing   that   the   quantity   of  predicates 
though  not  distinctly  expressed,   is  recogn.sed,  and  holdm, 
rt  is  .he  p..  or  U.C  ".o  „^.  »P;j-"J»S 
whatever  is  imphcit  in  thought,     ha%e  proposea 
the   quantity  of  predicates   by  predes.gnafon,   thus       Son^e 

„,en  are  some  wise  (beings)';  '-"f  »>-.;^^/°'  "fhe  Pre- 
(beings)';  etc.     This  is  called  the  Quantification  of  the  Pre 
d   1,  a,;d  leads  to  some  modifications  of  Deductive  Lo^c 
which  will  be  referred  to,  but  not  developed,  hereafter.     (See 

^  V  ^AsIo'Quahty,  propositions  are  either   Affirmative  or 
NeUivf   An  Affirm'ative  Proposition  is,  —y,  one  whose 
copula  is  affirmative  (or,  has  no  negative  sign),  as  SsP,Al 
Jn-are -partial  to  themselves.     A  Negative  Iropo stion 
one  whose  copula   is  negative  (or,  has  a   -Sa --  -g").  ^^ 
5  is  not  P  Sole  men-are  not-proof  agamst  flattery.     ^\  hen, 
fned  a  Negative  Proposition  is  of  Universal  Qu-tay  " - 
stated  thus :  No  S  is  P,  No  men  are  proof  agaunt  flatter   , 
t:t  t  this  case,  the  detachment  of  the  negative  sign  fron^h 
copula  and  its  association  with  the  subject  is  merely  an  acaden 
of  our  idiom  ;  the  proposition  is  the  same  as  ^/(  J-j;  j/ 
Proof  a^^ainst  flattery.     It  must  be  distinguished,  therefore 
fTrlh  an  efpres^ion  as  Not  every  -«  »  f^f  ^if 
flatterr  :  for  here  the  negative  sign  really  qualifies  the  sub^c 
and  the  proposition  is  Particular,  being  equivalent  to  Some 
men  are  not  proof  against  flattery.  -^u   ,u.  Predicate 

When  the  negative  sign  is  associated  with  the  Predicate 
so   as   to   make   this   an  Infinite  Term  (chap.  iv.  §  8) 
p°oposition  is  called  an  Infinite  Proposition  (though,  perhaps, 
Se  tL   and  the   Proposition   might   be   better   called  In- 
■    defiS,  as   S  is   not-P  (or  ,),  All  men   are-tncafaMe  of 
resisting  flattery,  or  are-notproof  against  flattery. 

•.•„„=  ™hen  the  copula  is  affirmative,  are,  formally. 

t^:^:^X^;^^tT.  hyphen.     It  has  heen  proposed, 


M 


THE   CLASSIFICATION   OF   PROPOSITIONS     49 


indeed,  with  a  view  to  superficial  simplification,  to  turn  all  Negatives 
into  Infinites,  and  thus  render  all  propositions  Affirmative  in  Quality. 
But  although  every  proposition  both  affirms  and  denies  something 
according  to  the  aspect  in  which  you  regard  it  (as  Snow  is  white  denies 
that  it  is  any  other  colour,  and  Snow  is  not  blue  affirms  that  it  is  some  other 
colour),  yet  there  is  a  great  difference  between  the  definite  affirmation 
of  a  true  Affirmative  and  the  vague  affirmation  of  a  Negative  or 
Infinite;  so  that  materially  an  Affirmative  Infinite  is  the  same  as  a 
Negative. 

Generally  Mill's  remark  is  true,  that  affirmation  and  denial  stand  for 
distinctions  of  fact  that  cannot  be  got  rid  of  by  manipulating  words. 
Whether  granite  sinks  in  water,  or  not ;  whether  the  rook  lives  to  be  a 
hundred,  or  not ;  whether  a  man  has  a  hundred  dollars  in  his  pocket, 
or  not ;  whether  human  bones  have  ever  been  found  in  tertiary  strata, 
or  not ;  such  alternatives  require  distinct  forms  of  expression.  At  the 
same  time,  it  may  be  granted  that  many  facts  admit  of  being  stated 
with  nearly  equal  propriety  in  either  quality,  as  No  man  is  proof  against 
flattery,  or  All  men  are  open  to  flattery. 

But  whatever  advantage  there  is  in  occasionally  changing  the  Quality 
of  a  proposition  may  be  gained  by  the  process  of  obversion  (chap.  vii. 
§  5)  ;  whilst  to  use  only  one  Quality  would  impair  the  elasticity  of 
logical  expression.  It  is  a  postulate  of  Logic  that  the  negative  sign  may 
be  transferred  from  the  copula  to  the  predicate,  or  from  the  predicate 
to  the  copula,  without  altering  the  sense  of  a  proposition ;  and  this  is 
justified  by  the  experience  that  not  to  have  an  attribute  and  to  be 
without  it  are  the  same  thing. 

§  3.  A.  I.  E.  O. — Combining  the  two  kinds  of  Quantity 
Universal  and  Particular,  with  the  two  kinds  of  Quality,  Affirma- 
tive and  Negative,  we  get  four  simple  types  of  proposition » 
which  it  is  usual  to  symboh'se  by  the  letters  A.  I.  E.  O.,  thus  : 
A.  Universal  Affirmative — All  S  is  P. 
I.  Particular  Affirmative — Some  S  is  P. 
E.  Universal  Negative^No  S  is  P. 
O.  Particular  Negative — Some  S  is  not  P. 
These  symbols  are  exceedingly  useful  in  abbreviating  the 
exposition    of  Logic;   and   they  should   be   so   learnt   as   to 
suggest  their  meaning  without  the  least  need   for   an   effort 
of  recollection.     As  an  aid  to  this,  obs<?rve  that  A.  and  I. 
are  the  first  two  vowels  in  affirmo  and  that  E.  and  O.  are 
the  vowels  in  nego. 

Those    Logicians    who    explicitly   quantify    the    Predicate 


50       LOGIC:   DEDUCTIVE   AND   INDUCTIVE 
obtain,  in  all,  eight  forms  of  Proposition  according  to  Quantity 

and  Quality  :  .  „  ^,  •     „  ^r 

U    Totototal  Affirmative— All  X  is  all  Y. 

A.  Toto-partial  Affirmative— All  X  is  some  Y. 
Y    Parti-total  Affirmative— Some  X  is  all  Y. 
I.  Parti-partial  Affirmative— Some  X  is  some  Y. 
E.  Totototal  Negative— No  X  is  any  Y. 
,.  Toto-partial  Negative-No  X  is  some  Y. 
O    Parti-total  Negative— Some  X  is  not  any  Y. 
CO.  Parti-partial  Negative  -Some  X  is  not  some  Y 
Here  A  I   E.  O.  correspond  with  those  similarly  symbolised 
in  the  usual  list,  merely  designating  in   the   predicates   the 
quantity  which  was  formerly  treated  as  implicit. 

§  4.  As  to  Relation,  propositions  are  either  Categorical  or 
Conditional.  A  Categorical  Proposition  is  one  in  which  the 
predicate  is  directly  affirmed  or  denied  of  the  subject  without 
any  limitation  of  time,  place,  or  circumstance,  extraneous  to 
the  subject,  as  A//  men  in  England  an  secure  of„ntue;m 
which  proposition,  though  there  is  a  limitation  of  place  (  in 
England '),  it  is  included  in  the  subject.  Of  this  kind  are 
nearly  all  the  examples  that  have  yet  been  given,  according  to 

the  form  S  is  P.  ,  j- 

A  conditional  proposition  is  so  called  because  the  predica^ 
tion  is  made  under  some  limitation  or  condition  not  included 
in  the  subject,  as  //  a  man  lives  in  England,  he  is  secure  of 
justice      Here  the  limitation  '  living  in  England  '  is  put  into  a 
conditional   sentence   extraneous  to  the  subject,   'he     repre- 
senting any  man.  ti     „ 
Conditional  propositions,  again,  are  of  two  kinds-Hypo- 
thetical and  Disjunctive.     Hypothetical  Propositions  are  those 
that  are  limited  by  an  explicit  conditional  sentence,  as  above, 
or  thus :  Jfjoe  Srnith  was  a  prophet,  his  follo^vers  have  been 
unjustly  persecuted.     Or  in  symbols  thus  : 

If  A  is,  B  is ; 
If  A  is  B,  A  is  C ; 
If  A  is  B,  C  is  D. 


t 

I 


I 


-t- 


fi : 


•r*- 


\ 


THE   CLASSIFICATION   OF   PROPOSITIONS     51 

Disjunctive  Propositions  are  those  in  which  the  condition 
under  which  predication  is  made  is  not  expUcit  but  only 
implied  under  the  disguise  of  an  alternative  proposition,  as 
Joe  Stnith  was  either  a  prophet  or  an  i?tipostor.  Here  there  is 
no  direct  predication  concerning  Joe  Smith,  but  only  a  predi- 
cation of  one  of  the  alternatives  conditionally  on  the  other 
being  denied,  as,  If  Joe  Smith  was  not  a  prophet,  he  was  an 
impostor;  or,  If  he  was  not  an  impostor,  he  was  a  prophet. 
Symbolically,  Conditionals  may  be  represented  thus  : 

A  is  either  B  or  C, 
Either  A  is  B  or  C  is  D. 
Now,  formally,  every  conditional  may  be  expressed   as   a 
Categorical.     For  our  last  example  shows  how  a  Disjunctive 
may   be   reduced   to   two   Hypothetical   (of   which    one    is 
redundant,    being    the    Contrapositive    of     the     other;    see 
chap.  vii).     And  a  Hypothetical  is  reducible  to  a  Categorical 
thus  :  If  rainfalls  on  St.  Swithin's  Day,  it  falls  every  day  for 
the  next  forty;  or,  in  other  words,   The  case  of  rain  falling 
on  St.  Swithin's  Day  is  a  case  of  rain  falling  for  the  next  forty. 
But  this,  though  the  common  plan  of  stating  the  Categorical 
equivalent,   is  portentously  clumsy.     Recalling  Mill's  remark 
that  the  essence  of  a  Hypothetical  is  to  state  that  one  proposi- 
tion (the  indicative)  may  be  inferred  from  the  other  (the  condi- 
tional) we  may  write  :   The  falling  of  rain  upon  St.  Swithin's  Day 
is  a  sii^n  of  its  falling  for  the  next  forty.  Or,  similarly.  Proof  of  Joe 
Smith's  prophetic  mission  is  a  proof  of  his  not  being  an  impostor. 
This  turning  of  Conditionals  into  Categoricals  is  called  a 
Change  of  Relation  ;  and  the  process  may  be  reversed  :  All  the 
wise  are  virtuous  may  be  written.  If  any  man  is  wise  he  is 
virtuous  ;  or,  again.  Either  a  man  is  not  wise  or  he  is  virkous. 
But  the  Categorical  form  is  usually  the  simplest. 

If,  then,  as  substitutes  for  the  corresponding  Conditionals,  Categori- 
cals are  formally  adequate,  though  sometimes  inelegant,  it  may  be  urged 
that  Logic  has  nothing  to  do  with  elegance ;  or  that,  at  any  rate,  the 
chief  elegance  of  science  is  economy,  and  that  therefore,  for  scientific 
purposes,  whatever  we  may  write  further  about  Conditionals  must  be 
an  ugly  excrescence.     The  scientific  purpose  of  Logic  is  to  assign  the 


5,        LOGIC  :   DEDUCTIVE  AND   INDUCTIVE 

c    „^f     ran  we  then  in  the  Conditional  form  prove  any- 
condit.ons  of  proof     Can  vve  then,  '"J  ,  Conditional 

thing  that  cannot  be  proved  in  the  Categoncai .    u 
require  to  be  itself  proved  by  any  method  not  -PP'f  ^'«  ,'°  '^^j^'j^'^j 
Todcal?    If  not,  why  go  on  with  the  d-cusston  of  Cond.Uonals^     H 

TZ^X^ter  o^  'all  cases  in  which';  for  to  raise  a  doubt 
whether  a  strlht  line  is  ever  conceived  to  fall  upon  another,  whether 
^dtes  are  ev^r  unsupported,  or  population  ever  increases,  .s  a  super- 
S  of  sc  P'cism'and  plainly  *«  hypothetical  form  has  nothtng  to 
do  with  the  proof  of  such  propositions,  nor  with  .nference  f  om  them. 

Jni  in  some  cases  the  conditional  form  may  be  useful  One  of 
the^focrursTherTit  is  important  to  draw  attention  to  the  cond.^ 
as  something  especially  requiring  exammation.  If  time  n  a  ressmg 
::.r  11  sfl.  <'e  eJ^mian  into  tUe  sun  If  ''- f-;^-;^  ca 
n.enana.u.c  had  better  sdl  railways  and  buy  lani_  »^«™  ^^J^^/^n 
form  draws  attention  to  the  ^^^^^^^^^^^^ ^  ^-eTa^Idl 
.":frt;"rh:'d:^nrf™  ^^^  h^ypothetlc  form  has 

no  hfng  to  do  with  them.    A  second  case  in  which  the  hypothetica    is 
nothing  to  a°  "'  J  statement  occurs  where  a  proposition 

Xr^apaSr  -^^^^^^^  and  to  future  time,  as ///*.«  6.  «  s,o«, 
ot  „m  J.  ^lall  mss  our  ficnic.  It  is  in  such  cases  that  the  ca  egorKal 
form  leems  most  strained  and  inelegant.  But  even  then  it  is  logically 
Idequate  and  the  true  reasons  why  Conditionals  have  to  be  discussed 
t  A  v^^rAinaftpr  are   that  it  is  usual  to  do   so,  that  students  are 

^ble  o  beXf  SouT'them,  and  (what  is  really  important)  that  they 
urnish  valuable  exercises  in  formal  thinking.    Most  people  find  them 
I^e  difficuU  to  manipulate  than  Categoricals,  and  therefore,  of  course, 
they  should  be  more  zealously  mastered. 

In  discussing  Conditional  propositions,  the  conditional 
sentence  of  a  Hypothetical,  or  the  first  alternative  of  a  D.s- 
iunctive,  is  called  the  Antecedent;  the  indicative  sentence  of  a 
Hypothetical,  or  the  second  alternative  of  a  Disjunctive,  is 

called  the  Consequent. 

Hypotheticals,  like  Categoricals,  may  be  classed  according 
to  Quantity  and  Quality.  Premising  that  the  quantity  of  a 
Hypothetical  depends  on  the  quantity  of  its  Antecedent 
(vvWch  determines  its  limitation),  whilst  its  quality  depends 


1 


I 


THE   CLASSIFICATION   OF   PROPOSITIONS     5^ 

on  the  quality  of  its  Consequent  (which  makes  the  predication), 
we  may  exhibit  four  forms  : 

A.  If  A  is  B,  Cis  D  ; 

I.  Sometimes  when  A  is  B,  C  is  D  ; 

E.  If  A  is  B,  Cisfiot  D; 

0.  Sometimes  when  A  is  B,  C  is  not  D, 
But  I.  and  O.  are  rarely  used. 

As  for  Disjunctives,  it  is  easy  to  distinguish  the  two  Quantities 

thus : 

A.  Either  A  is  B  or  C  is  D  ; 

1.  Someii?fies  either  A  is  B  or  C  is  D. 

But  I  is  rarely  used.  The  distinction  of  Quality,  however,  cannot 
be  made  :  there  are  no  true  negative  forms.     If  we  write  : 

Neither  is  A  B,  nor  C  D, 
there  is  here  no  alternative  predication,  but  only  an  Exponible, 
equivalent  to  No  A  is  B,  and  No  C  is  D,     And  if  we  write  : 

Either  A  is  not  B,  or  C  is  not  D, 
this  is  affirmative  as  to  the  alternation,  and  is  for  all  methods 
of  treatment  equivalent  to  x\. 

Logicians  are  divided  in  opinion  as  to  the  interpretation  of  the  con- 
junction •  either,  or  '  ;  some  holding  that  it  means  'not  both    others 
that  it  means  '  it  may  be  both.'     Grammatical  usage  upon  which  the 
question  is  sometimes  argued,  does  not  seem  to  be  established  in  favour 
of  either  view.     If  we  say  A  man  so  precise  in  his  walk  and  conversation  ts 
cither  a  saint  or  a  consummate  hypocrite;  or.  again.  One  who  is  happy  vi  a 
solitary  life  is  either  more  or  less  than  man  ;  we  cannot  in  such  ^ase^  mean 
that  the  subject  may  be  both.     On  the  other  hand  if  it  be  said  that^^. 
author  of  A  Tale  of  a  Tub  is  either  a  misanthrope  or  a  dyspeptic  the  alterna- 
tives are  not  incompatible.     Or.  again,  given  that  X  is  either  a  lunatic, 
a  lover,  or  a  poet,  the  three  predicates  have  much  congruity 

It  has  been  urged,  however,  that  in  Logic,  language  should  be  made 
as  exact  and  definite  as  possible,  and  that  this  requires  Jhe  ^^^f^jy; 
interpretation  '  not  both.'  But  it  seems  a  better  argument,  that  Logic, 
as  the  science  of  evidence,  must  not  assume  more  than  is  given .  and 
therefore,  to  be  on  the  safe  side,  must  in  doubtful  cases  assume  the 
least  iust  as  it  generally  assumes  a  preindesignate  term  to  be  ot  par- 
tlclr  quantity.'  According  to  this  argument.  •  either,  or    means    one. 

'^Ht:t?  lef  both  the  alternative  propositions  have  the  same 
subject,  as  either  A  is  B,  or  A  is  C,  if  the  two  predicates  are  contrary  or 


54        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

contradictory  terms,  they  cannot  in  their  nature  be  P^edicable  in  the 
same  way  of  the  same  subject  (as  e.g..  saint  and  hypocnte)    and  there 
fore,  in  such  a  case  '  either,  or  ■  means  one  or  the  "'l?^'.^"^"' "°'  b°*  ';. 
the  same  relation.     Hence  it  seems  necessary  to  admit  '^a    the  con 
junction  •  either,  or  '  may  sometimes  require  one  '".t«^P^«'^'°"' Xr 
times  the  other ;  and  the  rule  seems  to  be  that  it  >"'Pl'«f  '^e  fur  her 
alternative  ■  or  both,'  except  when  both  alternatives  have  the  =am«  ^"t'- 
ject  whilst  the  predicates  are  contraries  or  <=°""*'^!<='°"^'-  .  "  '^^ 
disjunctive  A  is  either  B  or  C  (B  and  C  being  contraries    '™Pl'«;  *^' 
both  alternatives  cannot  be  true,  it  can  only  be  adequately  rendered  in 
Hypotheticals  by  the  two  forms-(i)  If  A  is  B.  it  is  not  C,  and  {2)1/ A 
is  not  B.  it  is  C.    But  if  the  disjunctive  A  is  either  B  orC(B  and  C  not 
being  contraries)  implies  that  both  may  be  true,  it  will  be  adequately 
translated  into  a  hypothetical  by  the  single  form,  If  A  ,s  "<"  ^J  '' "  Y 
We  cannot  translate  it  mio-If  A  is  B.  it  is  not  C ;  for  by  o"-;  »PP°;'- 
tion  if  •  A  is  B  ■  is  true,  it  does  not  follow  that  '  A  is  C  must  be  fa  se. 

It'may  be  observed  that  these  conditional  forms  often  cojer  assertions 
that  are  not  true  complex  propositions,  but  arguments  abbreviated  and 
rhetorically  disguised.    The  hypothetical,  •  If  Plato  was  not  mistaken 
poets  are  dangerous  citizens,'  may  be  considered  as  an  argument  agamst 
the  laureateship,  and  may  be  expanded  (informally)  thus:    All  Plato  s 
opinions  deserve  respect ;  one  of  them  was  that  poets  are  bad  citizens^ 
therefore,  it  behoves  us  to  be  chary  of  encouraging  poetry      Or  take 
the  disjunctive,  •  Either  Bacon  wrote  the  works  ascribed '°  Shak^^P^^'^^ 
or  there  were  two  men  of  the  highest  genius  in  the  same  age  and 
country.'    This  means  that  it  is  not  likely  there  should  be  two  such  men, 
that  we  are  sure  of  Bacon,  and  therefore  ought  to  give  him  all  the  glory 
Now,  if  it  is  the  part  of  Logic  •  to  make  explicit  in  language  all  that  is 
impl  cit  in  thought,'  or  to  put  arguments  into  the  form  in  which  they  can 
best  be  examined,  such  propositions  as  the  above  ought  to  be  analysed 
in  the  way  suggested,  and  refuted  according  to  their  real  intention. 

§  5  As  to  Modality,  propositions  are  divided  into  Pure  and 
Modal  A  Modal  proposition  is  one  in  which  the  predicate  is 
affirmed  or  denied,  not  simply  but  am  modo,  with  a  qualifica- 
tion And  some  Logicians  have  considered  any  adverb  occur- 
ring in  the  predicate,  or  any  sign  of  past  or  future  tense,  enough 
to  "constitute  a  modal :  as  '  Petroleum  is  dangerously  inflam- 
mable '  •  '  English  will  be  the  universal  language.'  But  far  the 
most  important  kind  of  modality,  and  the  only  one  we  need 
consider,  is  that  which  is  signified  by  some  qualification  of 
the  predicate  as  to  the  degree  of  certainty  with  which  it  is 
affirmed  or  denied.     Thus,  '  The  bite  of  the  cobra  is  probably 


THE  CLASSIFICATION  OF  PROPOSITIONS     55 

mortal,'  is  called  a  'Contingent'  or  'Problematic'  Modal: 
'  Water  is  certainly  composed  of  oxygen  and  hydrogen '  is  an 
Assertory  or  Certain  Modal:  'Two  straight  lines  cannot 
enclose  a  space '  is  a  Necessary  or  Apodeictic  Modal  (the 
opposite  being  inconceivable).    Propositions  not  thus  qualified 

are  called  Pure. 

Modal  propositions  have  had  a  long  and  eventful  history,  but  they 
have  not  been  found  tractable  to  the  resources  of  ordinary  Logic,  and 
are  now  generally  neglected  by  the  authors  of  text-books.    Accordingly. 
I  shall  not  enlarge  upon  the  merely  logical  treatment  of  them  in  the 
present  work.     No  doubt  such  propositions  are  common  m  ordinary 
discourse,  and  in  some  rough  way  we  combine  them  and  draw  inferences 
from  them.     It  is  understood  that  a  combination  of  assertory  or  of 
apodeictic  premises  may  warrant  an  assertory  or  an  apodeictic  conclu- 
sion •   but  that  if  we  combine  either  of  these  with  a  problematic  pro- 
position our  conclusion  becomes  problematic ;  whilst  the  combination 
of  two  problematic  premises  gives  a  conclusion  less  certain  than  either. 
But  if  we  ask  '  How  much  less  certain  ? '  we  are  left  to  sheer  guessing. 
That   the  modality  of  a  conclusion   follows  the  less  certain  of  the 
propositions  combined,  is  inadequate  for  scientific  guidance  ;  so  that,  as 
ordinary  Logic  can  get  no  further  than  this,  it  is  now  generally  agreed 
to  abandon  the  discussion  of  Modals.     The  true  scientific  course  with 
regard  to  them  is,  to  endeavour  to  determine  the  degree  of  certainty 
attaching   to  a  proposition  by  collecting  statistics  with  regard  to  it. 
Thus  instead  of  '  The  cobra's  bite  is  probably  fatal,'  we  might  find  that 
it  is  fatal  80  times  in  loo.     Then,  if  we  know  that  of  those  who  go  to 
India  3  in  looo  are  bitten,  we  can  calculate  what  the  chances  are  that 
any  one  going  to  India  will  die  of  a  cobra's  bite  (chap.  xx.). 

§  6.  Verbal  and  Real  propositions.—Another  important 
division  of  propositions  turns  upon  the  relation  of  the  predi- 
cate to  the  subject  in  respect  of  their  connotations.  We 
saw  when  discussing  Relative  Terms,  that  the  connotation  of 
one  term  often  implies  that  of  another ;  sometimes  recipro- 
cally, like  '  master  '  and  '  slave ' ;  or  by  inclusion,  like  species 
and  genus ;  or  by  exclusion,  like  contraries  and  contradictories. 
When  terms  so  related  appear  as  subject  and  predicate  of  the 
same  proposition,  the  result  is  often  tautology- ^.^-.,  The  master 
has  authority  over  his  slave;  A  horse  is  an  animal;  Red  is  not 
blue  ;  British  is  not  foreign.  Whoever  knows  the  meaning  of 
'  master,'  '  horse,'  '  red,'  '  British,'  learns  nothing  from  these 


I 


56        LOGIC:    DEDUCTIVE    AND    INDUCTIVE 

propositions.  Hence  they  are  called  Verbal  propositions,  as 
only  expounding  the  sense  of  words,  or  as  if  they  were  propo- 
sitions only  by  satisfying  the  forms  of  language,  not  by  fulfilling 
the  function  of  propositions  in  conveying  a  knowledge  of  facts. 
They  are  also  called  '  Analytic '  and  '  Explicative ',  because 
they  separate  and  disengage  the  elements  of  the  connotation 
of  the  subject.  Doubtless,  such  propositions  are  very  useful  to 
one  who  does  not  know  the  language ;  and  Definitions,  which 
are  verbal  propositions  whose  predicates  analyse  the  whole 
connotations  of  their  subjects,  are  indispensable  instruments 
of  science  (see  chap.  xxii). 

On  the  other  hand,  when  there  is  no  such  direct  relation 
between  subject  and  predicate  that  their  connotations  imply 
one  another,  but  the  predicate  connotes  something  that 
cannot  be  learnt  from  the  connotation  of  the  subject,  there 
is  no  longer  tautology,  but  an  enlargement  of  meaning— ^•a'-., 
Masters  are  degraded  by  their  slaves;  The  horse  is  the  tioblest 
animal ;  Red  is  the  favourite  colour  of  the  British  army.  Such 
propositions  are  called  Real,  Synthetic,  or  Ampliaiive,  because 
they  are  propositions  for  which  a  mere  understanding  of  their 
subjects  would  be  no  substitute,  since  the  predicate  adds  a 
meaning  of  its  own  concerning  matter  of  fact. 

It  has  been  seriously  questioned  whether  a  verbal  propo- 
sition deserves  to  be  called  a  proposition  at  all.  We  may  ask 
whether,  to  any  one  who  understands  the  language,  a  verbal 
proposition  can  ever  be  an  inference  or  conclusion  from 
evidence;  or  whether  a  verbal  proposition  can  ever  furnish 
grounds  for  an  inference,  which  might  not  just  as  well  be 
found  in  the  meaning  of  the  subject?  It  hardly  belongs  to 
such  a  book  as  this  to  determine  such  disputed  questions;  but 
we  shall  see  hereafter  that,  without  an  answer  to  them,  some 
important  problems  must  remain  unsolved.  The  whole  subject  of 
real  and  verbal  propositions  will  inevi  tably  recur  in  the  chapters  on 
Definition  ;  but  Verbal  Propositions  are  such  common  blemishes 
in  composition,  and  such  frequent  and  fatal  pitfalls  in  argument 
that  attention  cannot  be  drawn  to  them  too  early  or  too  often. 


\ 


\i .. 


1! 


CHAPTER  VI 
CONDITIONS   OF  IMMEDIATE   INFERENCE 

§  I.  The  word  Inference  is  used  in  two  different  senses, 
which  are  often  confused  but  should  be  carefully  distinguished. 
In  the  first  sense,  it  means  a  process  of  thought  or  reasoning 
by  which  the  mind  passes  from  facts  or  statements  presented, 
to  some  opinion  or  expectation.  The  data  may  be  very  vague 
and  slight,  prompting  no  more  than  a  guess  or  surmise;  as 
when  we  look  up  at  the  sky  and  form  some  expectation  about 
the  weather,  or  from  the  trick  of  a  man's  face  entertain  some 
prejudice  as  to  his  character.  Or  the  data  may  be  important 
and  strongly  significant,  like  the  footprint  that  frightened 
Crusoe,  or  as  when  news  of  war  makes  the  City  expect  that 
Consols  will  fall.  These  are  examples  of  the  act  of  inferring, 
or  of  inference  as  a  process ;  and  with  inference  in  this  sense 
Logic  has  nothing  to  do ;  it  belongs  to  Psychology  to  explain 
how  it  is  that  our  minds  pass  from  one  perception  or  thought 
to  another  thought,  and  how  we  come  to  conjecture,  conclude 
and  believe  {(/".  chap.  i.  §  6). 

In  the  second  sense,  inference  means  not  this  process  of 
guessing  or  opining,  but  the  result  of  it ;  the  surmise,  opinion, 
or  belief  when  formed ;  in  a  word,  the  conclusion  :  and  it  is  in 
this  sense  that  Inference  is  treated  of  in  Logic.  The  subject- 
matter  of  Logic  is  an  inference,  judgment  or  conclusion  con- 
cerning facts,  embodied  in  a  proposition,  which  is  to  be  ex- 
amined in  relation  to  the  evidence  that  may  be  adduced  for  it, 
in  order  to  determine  whether,  or  how  far,  the  evidence 
amounts  to  proof.     Logic  is  the  science  of  Reasoning  in  the 


58        LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

sense  in  which  '  reasoning'  means  giving  reasons,  for  it  shows 
:it  sort  of  reasons  aregood.    Whilst  Psychology  exp.a.ns  how 
the  mind  goes  forward  from  data  to  conclusions,  Loj  'akes  a 
conclusion  and  goes  back  to  the  data,  .nqunmg  -hethe      1  o^e 
data  together  with  any  other  evidence  (facts  or  prmc.ple.)  that 
can  be  collected,  are  of  a  nature  to  warrant  the  conclusion.     I 
w'  think  that  the  night  will  be  stormy,  that  A.  Schu.tze  rs  of  a- 
amiable  disposition,  that  water  expands  m  free.mg,  o^  '^at  one 
n,eans  to  national  prosperity  is  popular  education,  and  w.  h   o 
know  whether  we  have  evidence  sufficient  to  justify  us  ,n  holding 
these  opinions,  Logic  can  tell  us  what  form  tl^^-'^ence  should 
assume  in  order  to  be  conclusive.     Observe :      say  what  /.^ 
the  evidence  should  assume,  not  that  Logic  tells  us  what  facts 
are  proper  evidence  in  any  of  these  cases  ;   that  ,s  a  question 
:  t'he  man  of  special  experience  in  life,  or  ^^^^^ 
business.     But  whatever  the  facts  are  that  constitute  the  ev, 
dence,  they  must,  in  order  to  prove  the  point,  adm  t  of  being 
stated  in  conformity  with  certain  principles  or  conditions    and 
of  these  principles  or  conditions  Logic  is  the  science.    It  deals. 
In,  not'with'the  subjective  process  of  inferring,  but  with  the 
objective  grounds  that  justify  or  discredit  the  >"f«ence. 

§  2  Inferences,  in  the  Logical  sense,  are  divided  into  t«o 
great  classes,  the  Immediate  and  the  Mediate,  according  to  the 
character  of  the  evidence  offered  in  proof  of  them^  In  fact  ^ 
speak  of  Inferences,  in  the  sense  of  conclusions,  as  immed  ate 
or  mediate  is  an  abuse  of  language,  derived  from  times  befo 

the  distinction  between  inference  as  P— ^^"f^  "l"^  ^"Jei 
result  was  generally  felt.  No  doubt,  we  ought  rather  to  speak 
of  Lmediate  and  Mediate  Evidence;  but  it  would  be  out  o 
place  in  a  manual  to  attempt  to  alter  the  usual  expressions  of 

'"  An  immediate  Inference,  then,  is  one  that  depends  for  its  proof 
upon  only  one  other  proposition  which  has  the  same,  or  more 
extensive  terms  (or  matter).    Thus  that '  one  means  to  nat.ona 
p  osped     is  popular  education '  is  an  immediate  inference   if 
^evidence  Zr  it  is  no  more  than  the  admission  that  'popular 


[ 


i\ 


CONDITIONS   OF   IMMEDIATE   INFERENCE      59 

education  is  a  means  to  national  prosperity ' :  Similarly,  it  is 
an  immediate  inference  that  *  Some  authors  are  vain,'  if  it  be 
granted  that  *  All  authors  are  vain.' 

An  Immediate  Inference,  indeed,  is  little  else  than  a  verbal 
transformation ;  and  some  Logicians  dispute  its  claims  to  be 
called  an  inference  at  all,  on  the  ground  that  it  is  identical 
with  the  pretended  evidence.  If  we  attend  to  the  meaning, 
say  they,  an  immediate  inference  does  not  really  express  any 
new  judgment ;  the  fact  expressed  by  it  is  either  the  same  as 
its  evidence,  or  is  even  less  significant.  If  from  No  men  are 
gods  we  prove  that  No  gods  are  men,  this  is  nugatory ;  if  we 
prove  from  it  that  Some  men  are  not  gods,  this  is  to  emasculate 
the  sense,  to  waste  valuable  information,  to  lose  the  command- 
ing sweep  of  our  universal  proposition. 

Still,  in  formal  Logic,  it  is  often  found  that  an  immediate 
inference  expresses  our  knowledge  in  a  more  convenient  form 
than  that  of  the  evidentiary  proposition,  as  will  appear  in  the 
chapter  on  Syllogisms  and  elsewhere.  And  in  transforming  a 
Universal  into  a  Particular  proposition,  as  No  men  are  gods, 
therefore.  Some  men  are  not  gods,  the  latter  statement,  though 
weaker,  is  far  more  easily  proved;    since   a   single   instance 

suffices. 

A  Mediate  Inference,  on  the  other  hand,  depends  for  its 
evidence  upon  a  plurality  of  other  propositions  (two  or  more) 
which  are  connected  together  on  logical  principles.      If  we 

argue — 

No  men  are  gods  ; 

Alexander  the  Great  is  a  man  ; 
.-.  Alexander  the  Great  is  not  a  god  : 
this  is  a  Mediate  Inference.  The  evidence  consists  of  two 
propositions  connected  by  the  term  '  man,'  which  is  common 
to  both  (a  Middle  Term),  mediating  between  'gods'  and 
'Alexander.'  Mediate  Inferences  comprise  Syllogisms  with 
their  developments,  and  Inductions;  and  to  discuss  them 
further  at  present  would  be  to  anticipate  future  chaplers.  We 
must   now   deal  with   the   principles  or  conditions  on  which 


Go        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

Immediate  Inferences  are  valid  :  commonly  called  the  "  Laws 
of  Thought." 

§  3.  The  Laws  of  Thought  are  conditions  of  the  logical 
statement  and  criticism  of  all  sorts  of  evidence ;  but  as  to 
Immediate  Inference,  they  may  be  regarded  as  the  only 
conditions  it  need  satisfy.  They  are  three  :  (i)  The  principle 
of  Identity  (usually  stated  as  '  Whatever  is,  is'  or  ' A  is  A')\ 
(2)  The  principle  of  Contradiction  {' Jt  is  impossible  for  the 
same  thing  to  be  and  ?iot  be,'  or  'A  is  not  not-A');  (3)  The 
principle  of  Excluded  Middle  {'Anything  must  either  be  or 
not  be,'  or  'B  is  either  A  or  not  A').  These  principles  are 
manifestly  not  '  laws '  of  thought  in  the  sense  in  which  *  law ' 
is  used  in  Psychology;  they  do  not,  like  the  laws  of  the 
association  of  ideas,  profess  to  give  an  account  of  the  actual 
mental  processes  that  uniformly  take  place  in  judgment  or 
reasoning.  If  they  were  such  natural  laws  of  thought,  it 
would  be  impossible  for  anybody  to  mistake  one  thing  for 
another  or  assume  that  the  same  thing  may  both  be  and 
not  be;  whereas  we  know  that  people  frequently  make  such 
mistakes.  In  relation  to  thought,  therefore,  these  principles 
can  only  be  regarded  as  laws  when  stated  as  precepts,  the 
observance  of  which  (consciously  or  not)  is  necessary  to 
clear  and  consistent  thinking :  e.g.,  Never  assume  that  the 
same  thing  can  both  be  and  not  be. 

However,  in  this  book  Logic  is  treated  as  the  science  of 
thought  only  as  embodied  in  propositions,  in  respect  of  which 
evidence  is  to  be  adduced,  or  which  are  to  be  used  as  evi- 
dence of  other  propositions ;  and,  accordingly,  the  above  laws 
or  principles  must  be  restated  as  the  conditions  of  consistent 
argument  in  such  terms  as  to  be  directly  applicable  to  propo- 
sitions. Now,  it  was  shown  in  the  chapter  on  the  connotation 
of  terms,  that  terms  are  assumed  by  Logicians  to  be  capable  of 
definite  meaning,  and  of  being  used  univocally  in  the  same 
context:  if,  or  in  so  far  as,  this  is  not  the  case,  we  cannot 
understand  one  another's  reasons,  nor  even  pursue  in  solitary 
meditation  any  coherent  train    of  argument.     We   saw,  too 


*'* 


CONDITIONS   OF   IMMEDIATE   INFERENCE      61 

that  the  meanings  of  terms  were  related  to  one  another : 
some  being  full  correlatives ;  others  partially  inclusive  one 
of  another,  as  species  of  genus ;  others  mutually  incompatible, 
as  contraries ;  or  alternatively  predicable,  as  contradictories. 
We  now  assume  that  propositions  are  capable  of  definite 
meaning  according  to  the  meaning  of  their  component  terms 
and  of  the  relation  between  them ;  that  the  meaning,  the  fact 
asserted  or  denied,  is  what  we  are  really  concerned  to  prove  or 
disprove ;  that  a  mere  change  in  the  words  that  constitute  our 
terms,  or  of  construction,  does  not  affect  the  truth  of  a  propo- 
sition as  long  as  the  meaning  is  not  altered,  or  (rather)  as  long 
as  no  fresh  meaning  is  introduced ;  and  that  if  the  meaning  of 
any  proposition  is  true,  any  other  proposition  that  denies  it  is 
false.  This  postulate  is  plainly  necessary  to  consistency  of 
statement  and  discourse ;  and  consistency  is  necessary,  if 
our  thought  or  speech  is  to  correspond  wi^h  the  unity  and 
coherence  of  Nature  and  experience  ;and  the  Laws  of  Thought 
or  Conditions  of  Immediate  Inference  are  an  analysis  of  this 
postulate; 

§  4.  The  principle  of  Identity  is  usually  written  symbolically 
thus  :  A  is  A  ;  not-A  is  ?wt-A.  It  assumes  that  something  is, 
and  that  it  may  be  represented  by  a  term.  We  need  not  here 
raise  any  metaphysical  question  whether  after  all  anything  can 
be  said  really  to  be,  to  be  self-identical  and  sempiternal.  Logic 
takes  for  granted  a  certain  relative  identity  and  persistence  of 
things.  Socrates  in  his  father's  workshop,  at  the  battle  of 
Delium  and  in  prison,  is  assumed  to  be  the  same  man 
denotable  by  the  same  name;  and  similarly,  elephant,  or 
justice,  or  fairy,  in  the  same  context,  is  to  be  understood 
of  the  same  thing  under  the  same  suppositio. 

But,  further,  it  is  assumed  that  of  the  same  thing  another 
term  may  be  predicated  again  and  again  in  the  same  sense. 
To  symbolise  this  we  ought  to  alter  the  usual  formula  for 
Identity  and  write  it  thus  :  If  B  is  A,  B  is  A  ;  if  B  is  not-A, 
B  is  not-A.  If  Socrates  is  wise,  he  is  wise ;  if  fairies  frequent 
the  moonlight,  they  do ;  if  Justice  is  not  of  this  world,  it  is 


62        LOGIC:   DEDUCTIVE    AND    INDUCTIVE 

not.  Whatever  affirmation  or  denial  we  make  concerning 
any  subject,  we  are  bound  to  adhere  to  it.  Of  course,  if 
our  assertion  turns  out  to  be  false,  we  must  not  adhere  to 
it;  but  then  we  must  repudiate  all  that  we  formerly  deduced 
from  it  and  begin  again  with  a  clean  slate. 

Again,  whatever  is  true  or  false  in  one  form  of  words  is 
true  or  false  in  any  other :  this  is  undeniable ;  but  in  formal 
Logic  it  is  not  very  convenient.     If  Socrates  is  wise,  is  it  an 
identity  to  say,  '  Therefore  the  master  of  Plato  is  wise ' ;  or, 
further,  that  he  'takes  enlightened  views  of  life'?     U  Every 
man  is  fallible,  is  it  an  identical  proposition  that  Every  man 
is  liable  to  error  1     It  seems  pedantic  to  demand  a  separate 
proposition  that  Fallible  is  liable  to  error.     But,  on  the  other 
hand,  the  insidious  substitution  of  one  term  for  another  spe- 
ciously identical,  is  a  chief  occasion  of  fallacy.     How  if  we  go 
on  to  argue :  therefore.  Every  man  is  apt  to  blunder,  prone  to 
confusion  of  thought,  addicted  to  self-contradiction  ?     Practi- 
cally, I  am  afraid  that  the  substitution  of  identities  must  be 
left  to  candour  and  good-sense  ;  and  may  they  increase  among 
us.     But   formal    Logic   is,  no   doubt,   safest  with   symbols; 
should,  perhaps,  content  itself  with  A  and  B ;   or,  at  least, 
hardly  venture  beyond  Y  and  Z, 

§  5.  The  principle  of  Contradiction  is  usually  written  sym- 
bolically, thus  .  A  is  not  not-A.     But,  since  this  formula  seems 
to  be  adapted  to  a  single  term,  and  we  want  one  that  is  applic- 
able to  propositions,  it  may  be  better  to  write  it  thus :  B  is  not 
both  A  and  not-A.     That  is  to  say  :  if  any  term  may  be  affirmed 
of  a  subject,  the  contradictory  term  may  be  denied  of  it  in  the 
same  relation.    A  leaf  that  is  green  on  one  side  of  it  may  be  not- 
green  on  the  other ;  but  it  is  not  both  green  and  not-green  on 
the  same  surface,  at  the  same  time,  and  in  the  same  light.     If 
a  stick  is  straight,  it  is  false  that  it  is  at  the  same  time  not- 
straight  :  having  granted  that  two  angles  are  equal,  we  must 
deny  that  they  are  unequal. 

But  is  it  necessarily  false  that  the  stick  is  crooked ;  must  we 
deny  that  either  angle  is  greater  or  less  than  the  other?     How 


CONDITIONS   OF   IMMEDIATE   INFERENCE     63 

far  is  it  permissible  to  substitute  any  other  term  for  the  formal 
contradictory?     Clearly,  the  principle  of  Contradiction  takes 
for  granted  the  principle  of  Identity  and  is  subject  to  the 
same  difficulties  in  its  practical  application.     As  a  matter  of 
fact  and  common  sense,  if  we  affirm  any  term,  we  are  bound 
to  deny  not  only  the  contradictory  but  all  synonyms  for  this, 
and  also  all  contraries  and  opposites ;   which,  of  course,  are 
included  in  its  contradictory.     But  who  shall  determine  what 
these   are?     Without  an   authoritative  Logical   Dictionary  to 
refer  to,  where  all  contradictories,  synonyms,  and  contraries 
may  be  found  on  record,  formal  Logic  will  hardly  sanction  the 
free  play  of  common  sense. 

The  principle  of  Excluded  Middle  is  usually  written  :  B  is 
either  A  or  not-A  ;  that  is,  if  any  term  be  denied  of  a  subject, 
the  contradictory  term  may  be  affirmed  in  the  same  relation. 
Of  course,  we  may  deny  that  a  leaf  is  green  on  one  side 
without  being  bound  to  affirm  that  it  is  not  green  on  the 
other.  But  in  the  same  relation  a  leaf  is  either  green  or  not 
green  ;  at  the  same  time,  a  stick  is  either  bent  or  not  bent.  If 
we  deny  that  A  is  greater  than  B,  we  must  affirm  that  it  is  not 
greater  than  B. 

Whilst,  then,  the  principle  of  Contradiction  (that  *  of  contra- 
dictory predicates,  one  being  affirmed,  the  other  is  denied ') 
might   seem    to   leave   open   a   third   or   middle   course,   the 
denying  of  both    contradictories,  the   principle   of  Excluded 
Middle  derives  its  name  from  the  excluding  of  this  middle 
course,    by   declaring   that   the   one   or    the   other    must    be 
affirmed.      Hence   the   principle   of   Excluded    Middle    does 
not  hold  good  of  mere  Contrary  Terms.     If  we  deny  that 
a  leaf  is  green,  we  are  not  bound  to  affirm  it  to  be  yellow; 
for  it  may  be  red;  and,  therefore,  we  may  deny  both   con- 
traries, yellow  and   green.      In   fact   two   contraries   do    not 
between  them  cover  the  whole  predicable  area,  but  contra- 
dictories do  :  the  form  of  their  expression  is  such  that  (within 
the  suppositio)  each  includes  all  that  the  other  excludes ;  so 
that  the  subject  (if  brought  within  the  suppositio)  must  fall 


64       LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

under  the  one  or  the  other.  It  may  seem  absurd  to  say  that 
Mont  Blanc  is  either  wise  or  not-wise ;  but  how  comes  your 
mind  so  ill-organised  as  to  introduce  Mont  Blanc  into  this 
strange  company?  Being  there,  however,  the  principle  is 
inexorable  :  Mont  Blanc,  alas  !  is  not-wise. 

In  fact,  the  principles  of  Contradiction  and  Excluded 
Middle  are  inseparable;  they  are  implicit  in  all  distmct 
experience,  and  may  be  regarded  as  indicating  the  two  aspects 
of  Negation.  The  principle  of  Contradiction  says  :  B  is  either 
A  or  not-A,  as  if  not- A  might  be  nothing  at  all ;  this  is  abstract 
negation.  But  the  principle  of  Excluded  Middle  says: 
Grantim^  that  B  is  not  A,  it  is  still  somethini^—n^mtXy,  not-A  ; 
thus  bringing  us  back  to  the  concrete  experience  of  a  con- 
tinuum in  which  the  absence  of  one  thing  implies  the 
presence  of  something  else.  Symbolically :  to  deny  that  B  is 
A  is  to  affirm  that  B  is  not  A,  and  this  only  differs  by  a  hyphen 
from  B  is  not-A.  But  if  any  one  holds  that  the  hyphen  makes 
all  the  difference,  I  give  it  up. 

These  principles,  which  were  necessarily  to  some  extent  antici- 
pated in  chap.  iv.  §  7,  the  next  chapter  will  further  illustrate. 

§  6.  But  first  we  must  draw  attention  to  a  maxim  (also 
already  mentioned),  which  is  strictly  applicable  to  Immediate 
Inferences,  though  (as  we  shall  see)  in  other  kinds  of  proof  it 
may  be  only  a  formal  condition  :  this  is  the  general  caution 
not  to  go  beyond  the  evidence.  An  immediate  inference 
ought  to  contain  nothing  that  is  not  contained  (or  formally 
implied)  in  the  proposition  by  which  it  is  proved.  With 
respect  to  quantity  in  denotation,  this  caution  is  embodied 
in  the  rule  '  not  to  distribute  any  term  that  is  not  given  distri- 
buted.' Thus,  if  there  is  a  predication  concerning  *  Some  S,' 
or  *  Some  men,'  as  in  the  forms  I.  and  O.,  we  cannot  infer  any- 
thing concerning  '  All  S,'  or  '  All  men  ; '  and,  as  we  have  seen, 
if  a  term  is  given  us  preindesignate,  we  are  generally  to  take  it 
as  of  particular  quantity.  Similarly,  in  the  case  of  affirmative 
propositions,  we  saw  that  this  rule  requires  us  to  assume  that 
their  predicates  are  undistributed. 


\\i 


CONDITIONS   OF   IMMEDIATE   INFERENCE     65 

As  to  the  grounds  of  this  maxim,  not  to  go  beyond  the 
evidence,  not  to  distribute  a  term  that  is  given  as  undistri- 
buted, it  is  one  of  the  things  so  plain  that  to  try  to  justify 
is  only  to  obscure  them.  We  might  indeed  say  that  such 
a  leap  from  the  particular  to  the  general  is  not  sanctioned  by 
any  of  the  three  Laws  of  Thought.  The  caution  against  it 
may  particularly  be  viewed  as  supplementary  to  the  principle 
of  Identity,  that  whatever  is  true  in  one  form  of  words  is  true 
in  any  other  :  since  if  for  '  Some  S  '  we  substitute  '  All  S  ',  we 
no  longer  have  the  same  sense  as  the  given  form  of  words.  It 
is  a  gratuitous  assumption,  a  mere  non-sequitur ;  and  if  any 
controvertist  demands  permission  to  make  it,  the  formal 
logician  can  only  "  hold  up  his  hands  in  respectful  amaze- 
ment." 

Still  we  must  here  state  explicitly  what  Formal  Logic 
assumes  to  be  contained  or  implied  in  the  evidence  afforded 
by  any  proposition,  such  as  'All  S  is  P '.  If  we  remember 
that  in  chap.  iv.  §  7,  it  was  assumed  that  every  term  may 
have  a  contradictory ;  and  if  we  bear  in  mind  the  principles 
of  Contradiction  and  Excluded  Middle,  it  will  appear  that 
such  a  proposition  as  '  Ail  S  is  P '  tells  us  something  not  only 
about  the  relations  of  '  S '  and  '  P ',  but  also  of  their  relations 
to  '  not-S  '  and  '  not  P  ' ;  as,  for  example,  that  '  S  is  not  not-P ', 
and  that  '  not-P  is  not-S.'  It  will  be  shown  in  the  next  chapter 
how  Logicians  have  developed  these  implications  in  series  of 
Immediate  Inferences. 

If  it  be  asked  whether  it  is  true  that  every  term,  itself 
significant,  has  a  significant  contradictory,  and  not  merely  a 
formal  contradictory,  generated  by  force  of  the  word  '  not,'  it  is 
difficult  to  give  any  better  answer  than  was  indicated  in  §§  3-5, 
without  venturing  further  into  metaphysics.  I  shall  merely 
say,  therefore,  that,  granting  that  some  such  term  as  'Uni- 
verse '  or  '  Being '  may  have  no  significant  contradictory,  if  it 
stand  for  '  whatever  can  be  perceived  or  thought  of ' ;  yet 
every  term  that  stands  for  less  than  '  Universe '  or  '  Being '  has 
of  course,  a  contradictory  which  denotes  the  rest  of  the  uni- 

E 


66       LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

verse.  And  since  every  argument  or  train  of  thought  is  carried 
on  within  a  special  '  universe  of  discourse '  or  under  a  certain 
supposition  we  may  say  that  within  the  special  universe  or  sup- 
positio  every  term  has  a  contradictory,  and  that  every  predication 
concerning  a  term  implies  some  predication  concerning  its  con- 
tradictory. 


CHAPTER  VII 


IMMEDIATE    INFERENCES 


§  I.  Under  the  general  title  of  Immediate  Inference 
Logicians  discuss  three  subjects,  namely.  Opposition,  Con- 
version, and  Obversion  ;  to  which  some  writers  add  other 
forms,  such  as  Whole  and  Part  in  Connotation,  Contraposi- 
tion, Inversion,  etc.  Of  Opposition,  again,  all  recognise  four 
modes  :  Subalternation,  Contradiction,  Contrariety  and  Sub- 
contrariety.  The  only  peculiarities  of  the  exposition  upon 
which  we  are  now  entering  are,  that  it  follows  the  lead  of  the 
three  Laws  of  Thought,  taking  first  those  modes  of  Immediate 
Inference  in  which  Identity  is  most  important,  then  those 
which  plainly  involve  Contradiction  and  Excluded  Middle; 
and  that  this  method  results  in  separating  the  modes  of  Oppo- 
sition, connecting  Subalternation  with  Conversion,  and  the 
other  modes  with  Obversion.  To  make  up  for  this  departure 
from  usage,  the  four  modes  of  Opposition  will  be  brought 
together  again  in  §  9. 

§  2.  Subalternation.— Propositions  of  the  forms  A.  and  I.  are 
said  to  be  Subalterns  in  relation  to  one  another,  and  so  are  E. 
and  O. ;  the  universal  of  each  quahty  being  distinguished  as 
subalternans,  and  the  particular  as  subalternate. 

It  follows  from  the  principle  of  Identity  that,  the  matter  of  the  pro- 
positions being  the  same,  if  A.  is  true  I.  is  true,  and  that  if  E.  is  true 
O.  is  true  ;  for  A.  and  E.  predicate  something  of  All  S  or  All  men  ■  and 
since  I.  and  O.  make  the  same  predication  of  Some  S  or  Some  men.  the 
sense  of  these  particular  propositions  has  already^een  predicated  in  A 
or  E.  If  ^//  5  is  P.  Some  S  is  P;  if  No  S  ts  P,  Some  S  is  not  P  •  or  if 
All  men  are  fond  of  laughing,  Some  men  are;  if  No  men  are  exempt  from 
ridicule,  Some  men  are  not. 


\ 


it 
) 


\ 


68        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

Similarly,  if  I.  is  false  A.  is  false ;  if  O.  is  false  E.  is  falye.  If  we  deny 
any  predication  about  Some  S,  we  must  deny  it  of  All  S;  since  in 
denying  it  of  Some,  we  have  denied  it  of  at  least  part  of  All ;  and  what- 
ever is  false  in  one  form  of  words  is  false  in  any  other. 

On  the  other  hand,  if  I.  is  true,  we  do  not  know  that  A.  is  ;  nor  if  O. 
is  true,  that  E.  is ;  for  to  infer  from  Some  to  All  would  be  going  beyond 
the  evidence.  We  shall  see  in  discussing  Induction  that  the  great 
problem  of  that  part  of  Logic  is,  to  determine  the  conditions  under 
which  we  may  in  reality  transcend  this  rule  and  infer  from  Some  to  All; 
though  even  there  it  will  appear  that,  formally,  the  rule  is  observed. 
For  the  present  it  is  enough  that  I.  is  an  immediate  inference  from  A., 
and  O.  from  E.  ;  but  that  A.  is  not  an  immediate  inference  from  I.,  nor 
E.  from  O. 

,/    §  3.  Connotative  Subalternation. — We  have  seen  (chap.  iv. 

^  6)  that  if  the  connotation  of  one  term  is  only  part  of  another's 

its  denotation  is  greater  and  includes  that  other's.      Hence 

genus  and  species  stand  in  subaltern  relation,  and  whatever  is 

true  of  the  genus  is  true  of  the  species  :  If  A//  animal  life  is 

dependent  on  vegetation^  All  human  life  is  dependent  on  zegeta- 

tion.     On  the  other  hand,  whatever  is  not  true  of  the  species 

or  narrower  term,  cannot  be  true  of  the  whole  genus :  If  it  is 

false  that  '  All  human  life  is  happy, ^  it  is  false  that  '  All  animal 

life  is  happy. ^ 

Similar  inferences  may  be  drawn  from  the  subaltern  relation 

of  predicates  ;  affirming  the  species  we  affirm  the  genus.     To 

take  Mill's  example,  if  Socrates  is  a  man,  Socrates  is  a  living 

creature.     On  the  other  hand,  denying  the  genus  we  deny  the 

species  :  if  Socrates  is  not  vicious,  Socrates  is  not  drunken. 

It  cannot  be  said  that  such  cases  as  these  are  generally  recognised 
by  Logicians  as  immediate  inferences  coming  under  the  principle  of 
Identity.  They  are  so  regarded  by  Mill  and  Bain  ;  but  probably  most 
authorities  upon  our  science  would  treat  them  as  imperfect  syllogisms, 
requiring  another  premise  to  legitimate  the  conclusion,  as  thus : 

All  animal  life  is  dependent  on  vegetation  ; 

All  human  life  is  animal  life ; 

Therefore,  All  human  life  is  dependent  on  vegetation. 
Or  again : 

All  men  are  living  creatures ; 

Socrates  is  a  man  ; 

Therefore,  Socrates  is  a  living  creature. 
The   decision   of   this   issue  seems  to  turn   upon   the   question    [cf. 


IMMEDIATE   INFERENCES 


69 


chap  vi  §  %)  how  far  a  logician  is  entitled  to  assume  that  the  terms  he 
uses  are' understood,  and  that  the  identities  involved  in  their  meanmgs 
will  be  recognised.     And  to  this  question,  for  the  sake  of  consistency 
one  of  two  answers  is  required,  failing  which  there  remams  the  rule  of 
thumb      First,  it  may  be  held  that  no  term  is  understood  except  those 
that  are  defined  in  expounding  the  science,  such  as  '  genus '  and  '  species, 
•connotation.'  and   -denotation.'     But  very  few  logicians  observe  this 
limitation;  few  would  hesitate  to  substitute  'not-wise     ^^J  J^^^^^^" 
Yet  by  what  right  ?     Malvolio  being  foolish,  to  prove  that  he  is  not 
wise,  we  may  construct  the  following  syllogism  : 

Foolish  is  not-wise ; 
Malvolio  is  foolish ; 
Therefore,  Malvolio  is  not-wise. 
Is  this  necessary  ?     If  not,  why  not? 

Secondly,  it  may  be  held  that  all  terms  may  be  assumed  as  under- 
stood (amongst  those  native  to  the  language)  unless  a  defini  ion  is 
challenged.  This  principle  will  justify  the  substitution  of  not-wise 
for  'foolish'  ;  but  it  will  also  legitimate  the  above  cases  (concerning 
'  human  life '  and  '  Socrates ')  as  immediate  inferences,  with  mnumerable 
others  that  might  be  based  upon  the  doctrine  of  relative  names  as  for 
example  The  hunter  missed  his  aim;  therefore.  The  prey  escaped.  And 
from  thi;  principle  it  will  further  follow  that  all  apparent  syllogisnis 
having  one  premise  a  verbal  proposition,  are  immediate  inferences  {cf 

r^sd;^connected  with  such  cases  as  the  above  are  those  mentioned 
by  Archbishop  Thomson  as  "  Immediate  Inferences  by  added  Determi- 
nants "  {Lau.  of  Thought,  §  87).  He  takes  the  case  :  '  A  negro  ts  afello^^ 
creature  ■  therefore,  A  negro  in  sujfering  is  a  fellow  creature  m  sujfermg. 
This  re;ts  upon  the  principle  that  to  increase  the  connotations  of  two 
terms  by  th^same  attribute  or  determinant  does  not  -^-^ ;^-^  ^;-- 
ship  of  their  denotations,  since  it  must  equally  dimmish  (if  at  all  the 
denotations  of  both  classes,  by  excluding  the  same  individuals,  if  any 
want  the  given  attribute. 

§  4.  Conversion  is  Immediate  Inference  by  transposing  the 
terms  of  a  given  proposition  without  altering  its  quality.  If 
the  quantity  is  also  unaltered,  the  inference  is  called  '  Simple 
Conversion  ' ;  but  if  the  quantity  is  changed  from  universal  to 
particular,  it  is  called  'Conversion  by  limitation'  or  'per 
accidens:  The  given  proposition  is  called  the  '  convertend ' ; 
that  which  is  derived  from  it,  the  '  Converse.' 

Departing  from  the  usual  order  of  exposition.  I  have  taken  up  Con- 
veys on  nexf  to  Subalternation.  because  it  is  generally  thought  to  res 
upon   the   principle   of  Identity,  and  because  it  seems  to  be  a  good 


\    N 


70        LOGIC:    DEDUCTIVE    AND    INDUCTIVE 

method  to  exhaust  the  forms  that  come  only  under  Identity  before  going 
on  to  those  that  involve  Contradiction  and  Excluded  Middle.  Some 
mdeed  dispute  the  claims  of  Conversion  to  illustrate  the  principle 
of  Identity ;  and  if  the  sufficient  statement  of  that  principle  be  •  A  is  A  ' 
I  am  at  a  loss  to  see  how  Conversion  or  any  other  mode  of  Inference 
can  be  referred  to  it.  But  if  we  state  it  as  above  (ch.  vi  §  3)  that 
u-hateyer  is  true  in  one  form  of  words  is  true  in  any  other,  there' is  no 
difhculty  in  applying  it  to  Conversion.  Thus,  to  take  the  conversion  of  I 

Some  S  IS  P ;    .-.  Some  P  is  S. 

Some  poets  are  men  of  business ;   .-.  Some  men  of  business  are  foets 
Here  the  convertend  and  the  converse  say  the  same  thing,  and  this  is 
true  if  that  is. 

We  have  then,  two  cases  of  Simple  Conversion  :  of  I.  (as  above)  and 
of  E,     For  E. :  ' 

No  S  is  P:   .'.  No  P  is  S. 

No  ruminants  are  carnivores ;  .-.  No  carnivores  are  ruminants 
In  converting  I.,  the  predicate  (P)  when  taken  as  the  new  subject  being 
preindesignate.  is  treated  as  particular,  according  to  the  rule  '  noi  to  -o 
beyond  the  evidence  '  (chap.  vi.  §  4) ;  and  in  converting  E..  the  predicate 
in  when  taken  as  the  new  subject,  is  treated  as  universal,  accordin-  to 
the  rule  in  chap.  iv.  §1.  ° 

A.  is  the  one  case  of  Conversion  by  limitation  : 
All  S  is  P;   .-.  Some  P  is  S. 
All  cats  are  animals;   .-.  Some  animals  are  cats. 
And  here  the  treatment  of  the  predicate  as  particular,  when  taking  it 
for  the  new  subject,  is  according  to  the  rule  in  chap.  iv.  §  i.     Palpably 
to  infer  that  All  animals  are  cats  would  never  do. 

O.  cannot  be  truly  converted.  If  we  take  the  proposition  •  Some  S  is 
not  P,  to  convert  this  \nio  No  P  is  S,  or  Some  P  is  not  S,  would  break  the 
rule  in  chap.  vi.  §  4 ;  since  S.  undistributed  in  the  convertend,  would  be 
distributed  in  the  converse.  If  we  are  told  that  Some  men  are  not  cooks 
we  cannot  infer  that  Some  cooks  are  not  men.  This  would  be  to  assume' 
that  'Some  men  '  are  identical  with  'All  men.' 

By  quantifying  the  predicate,  indeed,  we  may  convert  O.  simply,  thus: 
Some  men  are  not  cooks   .-.   No  cooks  are  some  men. 
And  the  same  plan  has  some  advantage  in  converting  A.  ■  for  by  the 
usual  method  per  accidens,  the  converse  of  A.  being  I.,  if  we  convert  this 
agam  it  is  still  I.,  and  therefore  means  less  than  our  original  convertend 
1  nus  : 

All  S  is  P  .-.   Some  P  is  S   :.   Some  S  is  P 
S^uch  knowledge,  as  that  All  S  (the  whole  of  it)  ts  P,  is  too  precious  a 
thing  to  be  squandered  in  pure  Logic. 

On  the  other  hand,  quantifying  the  predicate,  if  we  convert  A   to  Y 
thus —  ■' 

All  S  is  P  .  \  Some  P  is  all  S-^ 


I 


IMMEDIATE    INFERENCES 


71 


H, 


i 


i 


I 


we  may  reconvert  Y.  to  A.  without  any  loss  of  meaning.  It  is  perhaps 
the  chief  use  of  quantifying  the  predicate  that,  thereby,  every  propo- 
sition is  capable  of  Simple  Conversion.  ^ 

§  5.  Obversion  (otherwise  called  Permutation  or  /Equipol- 
lence)  is  Immediate  Inference  by  changing  the  quality  of  the 
given  proposition  and  substituting  for  its  predicate  the  con- 
tradictory term.  The  given  proposition  is  called  the  'obver- 
tend '  and  the  inference  from  it  the  *  obverse.'  Thus  the 
obvertend  being — Some  philosophers  are  consistent  reasonerSy 
the  obverse  will  be — Some  philosophers  are  not  inconsistent 
reasoners. 

The  legitimacy  of  this  mode  of  inference  follows,  in  the 
case  of  affirmative  propositions,  from  the  principle  of  Contra- 
diction, that  if  any  term  be  affirmed  of  a  subject,  the  contra- 
dictory term  may  be  denied  (chap.  vi.  §  3).  To  obvert  affirma- 
tive propositions,  then,  the  rule  is — Add  the  negative  sign  to 
the  copula,  and  for  the  predicate  substitute  its  contradictory, 
A.     All  S  is  P  :.  No  S  is  not-P 

All  men  are  fallible  :.  No  men  are  infallible. 
I.     Some  S  is  P  :.  Some  S  is  ?iot  not-P 

Some  philosophers  are  consistent  :.  So?ne  philosophers 
are  not  inconsistent. 
In  agreement  with  this  mode  of  inference,  we  have  the  rule 
of  modern    English  grammar,  that  'two  negatives  make  an 
affirmative.' 

Again,  since  by  the  principle  of  Excluded  Middle,  if  any 
term  be  denied  its  contradictory  may  be  affirmed,  to  obvert 
negative  propositions,  the  rule  is— Remove  the  negative  sign 
from  the  copula,  and  for  the  predicate  substitute  its  contra- 
dictory. 

E.     No  S  is  P  :.  All  S  ts  not-P 

No  matter  is  destructible  :.  All  matter  is  indestructible. 

O.     So??ie  S  is  not  P  :.  So??ie  S  is  not-P 

Some  virtue  is  not  attainable  :.  Some  virtue  is  unattainable. 

Thus,  by  obversion,  each  of  the  four  propositions  retains  its  quantity 
but  changes  its  quality  :  A.  to  E.,  I.  to  O.,  E.  to  A..  O.  to  I.  And  all  the 
obverses  are  Infinite  Propositions,  the  affirmative  infinities  having  the 


72        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

sense    of  negatives,  and   the  negative  infinities  having  the  sense  of 
amrmatives. 

Again,  having  obtained  the  obverse  of  a  given  proposition,  it  may  be 
desirable  to  recover  the  obvertend  ;  or  it  may  at  any  time  be  requisite 
to  change  a  given  Infinite  into  the  corresponding  direct  Affirmative  or 
Negative  ;  and  in  such  cases  the  process  is  still  obversion.  Thus  if  No 
S  IS  not.p  be  given  us  to  recover  the  obvertend  or  to  find  the  correspond- 
ing Affirmative;  the  proposition  being  formallv  Negative,  we  applv  the 
rule  for  obverting  Negatives :  •  Remove  the  negative  sign  from  the 
copula,  and  for  the  predicate  substitute  its  contradictory  '  This  yields 
the  affirmative  All  S  is  P.  Similarly,  to  obtain  the  obvertend  of  ^//  5  is 
not-P,  apply  the  rule  for  obverting  Affirmatives ;  and  this  yields  No  S 
iS  P. 

§  6.  Contrariety.— We  have  seen  in  chap.  iv.  §  8,  that  con- 
trary terms  are  those  which  are  never  both  predicable  in  the 
same  way  of  the  same  subject,  whilst  perhaps  neither  may  be 
predicable  of  it.     Similarly,  Contrary  Propositions  are  defined 
as  those  that   are  never   both   true  together,   whilst  perhaps 
neither  may  be  true;   or,  in  other  words,  both  may  be  false. 
This  is  the  relation  between  A.  and  E.  when  concerned  with  the 
same  matter  :  as  A.— A//  meN  are  ivise :  E.—No  me?i  are  wise. 
Such  propositions  cannot  both  be  true ;  but  they  may  both  be 
false,  for  some  men  may  be  wise  and  some  not.     Contrary 
relation  may  be  viewed  as  according  with  the  principle  of  Con- 
tradiction :  if  it  may  be  affirmed  that  Ail  me?i  are  wise,  it  may 
be  denied  that  All  fnen  are  not-wise :  and  this  is  the  obverse 
of  No  men  are  wise,  which  therefore  may  also  be  denied. 

At  the  same  time  we  cannot  apply  to  A.  and  E.  the  principle 
of  Excluded  Middle,  so  as  to  show  that  one  of  them  must  be 
true  of  the  same  matter.  For  if  we  deny  that  All  men  are 
wise,  we  do  not  necessarily  deny  the  attribute  '  wise '  of  each 
and  every  man  :  to  say  that  Not  all  are  wise  may  mean  no 
more  than  that  Some  are  not.  This  gives  a  proposition  in  the 
form  of  O. ;  which,  as  we  have  seen,  does  not  imply  its  subal- 
ternans,  E. 

If,  however,  two  Singular  Propositions,  having  the  same 
matter,  but  of  different  quality,  are  to  he  treated  as  universale 
and  therefore  as  A.  and  E.,  they  are,  nevertheless,  contradic- 


IMMEDIATE   INFERENCES 


73 


\ 


tories  and  not  merely  contraries  ;  for  one  of  them  must  he  false 
and  the  other  true. 

§  7.  Contradiction,  however,  is  a  relation  between  two  pro- 
positions analogous  to  that  between  contradictory  terms,  such, 
namely,  that  one  of  them  is  false  and  the  other  true.  This  is 
the  case  with  the  forms  A.  and  O.,  and  E.  and  I.,  in  the  same 
matter.  If  it  be  true  that  All  men  are  wise,  it  is  false  that 
Some  men  are  not  wise  (equivalent  by  obversion  to  Some  men 
are  nof-2vise) ',  or  else,  since  the  *  Some  men '  are  included  in 
the  '  All  men,'  we  should  be  predicating  of  the  same  men  that 
they  are  both  '  wise  '  and  *  not-wise ' ;  which  would  violate  the 
principle  of  Contradiction.  Similarly,  No  men  are  wise,  being 
by  obversion  equivalent  to  All  men  are  7iot-wise,  is  incom- 
patible with  Some  men  are  wise,  by  the  same  principle  of  Con- 
tradiction. 

But,  again,  if  it  is  false  that  All  men  are  wise,  it  is  always 
true  that  Some  are  not  wise  ;  for  though  in  denying  that  *  wise  ' 
is  a  predicate  of  '  All  men '  we  do  not  deny  it  of  each  and 
every  man,  yet  we  deny  it  of  '  Some  men.'  Of  '  Some  men,' 
therefore,  by  the  principle  of  Excluded  Middle,  '  not-wise '  is 
to  be  affirmed ;  and  Some  men  are  not-wise,  is  by  obversion 
equivalent  to  Sofne  7nen  are  not  wise.  Similarly,  if  it  is  false 
that  No  jnen  are  wise,  which  by  obversion  is  equivalent  to  All 
men  are  7iot-wise,  then  it  is  true  at  least  that  So77ie  77ien  are 
wise, 

I  may  here  observe  that  by  extending  and  enforcing  the 
doctrine  of  relative  terms,  certain  other  inferences  are  implied 
in  the  contrary  and  contradictory  relation  of  propositions.  We 
have  seen  in  chap,  iv.,  that  the  contradictory  of  a  given  term 
includes  all  its  contraries  :  *  not-blue,'  for  example,  includes 
red  and  yellow.  Flence,  since  The  sky  is  blue  becomes  by 
obversion.  The  sky  is  7iot  7tot-blue,  we  may  also  infer  The  sky  is 
7iot  red,  etc.  From  the  truth,  then,  of  any  proposition  predica- 
ting a  given  term,  we  may  infer  the  falsity  of  all  propositions 
predicating  the  contrary  terms  in  the  same  relation.  But,  on 
the  other  hand,  from  the  falsity  of  a  proposition  predicating  a 


74        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

given  term,  we  cannot  infer  the  truth  of  the  predication  of  any 
particular  contrary  term.  If  it  is  false  that  The  sky  is  red,  we 
cannot  formally  infer  that  The  sky  is  blue  (cf.  chap.  vi.  §  3). 

§  8.  Sub-contrariety  is  the  relation  of  propositions,  con- 
cerning the  same  matter,  that  may  both  be  truth  but  are  never 
both  false.  This  is  the  case  with  I.  and  O.  If  it  be  true  that 
Some  me,i  are  7vise,  it  may  also  be  true  that  Some  {other)  men 
are  not  tvise.  This  follows  from  the  maxim  in  chap.  vi.  §  4 
not  to  go  beyond  the  evidence. 

For  if  it  he  true  that  Some  men  are  wise,  it  may  indeed  be  true  that  All 
are  (this  hein-  the  siibahernans) :  and  if  All  are,  it  is  (by  contradiction) 
false  that  Some  are  not;  but  as  we  are  only  told  that  Some  men  are.  it  is 
illicit  to  infer  the  falsity  of  Some  are  not,  which  could  only  be  justified  by 
evidence  concerninf,^  All  men. 

But  if  it  be  false  that  Some  men  are  vise,  it  is  true  that  Some  men  are  not 
wise:  for,  by  contradiction,  if  Some  men  are  wise  is  false,  No  men  are  wise 
IS  true :  and,  therefore,  by  subalternation,  Some  men  are  not  wise  is  true. 

§  9.  The  Square  of  Opposition.— By  their  relations  of 
Subalternation,  Contrariety,  Contradiction,  and  Sub-contrariety, 
the  forms  A.  I.  E.  O.  (having  the  same  matter)  are  said  to  stand 
in  Opposition  :  and  it  is  traditional  amongst  Logicians  to  re- 
present these  relations  by  a  square  having  A.  I.  E.  O.  at  its 
corners,  thus  : 


A. 


Contraries 


fi: 


en 

CD 
(A 


% 
^^. 


.<" 


^ 


c^ 


.^^ 


5-  \ 


tfi 
or 

CO 


I, 


Sub-contraries 


®; 


As  an  aid  to  the  memory,  this  diagram  is  useful ;  but  as  an  attempt 
to  represent  the  logical  relations  of  propositions,  it  is  useless,  and  indeed, 


• 


f 


IMMEDIATE    INFERENCES 


75 


misleading.  For,  standing  at  corners  of  the  same  square.  A.  and'E.,  A. 
and  I.,  E.  and  O.,  and  I.  and  O.,  seem  to  be  couples  bearing  tht  same 
relation  to  one  another ;  whereas  we  have  seen  that  their  relations  are 
entirely  different.  The  following  traditional  summary  of  their  relations 
in  respect  of  truth  and  falsity,  is  much  more  to  the  purpose : 
(i)  If  A.  is  true.  I.  is  true,  E.  is  false,  O.  is  false. 

(2)  If  A.  is  false,  I.  is  unknown,  E.  is  unknown,  O.  is  true. 

(3)  If  I.  is  true,  A.  is  unknown,  E.  is  false,  O.  is  unknown. 

(4)  If  I.  is  false,  A.  is  false.  E,  is  true,  O.  is  true. 

(5)  If  E.  is  true,  A.  is  false.  I.  is  false.  O.  is  true. 

(6)  If  E.  is  false.  A.  is  unknown,  I.  is  true,  O.  is  unknown. 

(7)  If  O.  is  true.  A.  is  false,  I.  is  unknown,  E.  is  unknown. 

(8)  If  O.  is  false,  A.  is  true,  I.  is  true,  E.  is  false. 

Where,  however,  as  in  cases  2,  3,  6.  7,  alleging  either  the  falsity  of 
Universals  or  the  truth  of  Particulars,  it  follows  that  two  of  the  three 
Opposites  are  unknown,  we  may  conclude  further  that  one  of  them  must 
be  true  and  the  other  false,  because  the  two  unknowns  are  always  Con- 
tradictories. 

§  10.  Secondary  modes  of  Immediate  Inference  are  obtained 
by  applying  the  process  of  Conversion  or  Obversion  to  the 
results  already  obtained  by  the  other  process.  The  best  known 
form  of  secondary  Immediate  Inference  is  the  Contrapositive, 
and  this  is  the  converse  of  the  obverse  of  a  given  proposition. 
Thus, 

A.  A/ I  S  is  P  :.  No  S  is  not-P  :.  No  not-P  is  S       ^v- 
I.  Sotne  S  is  P  :.  Some  S  is  not  not-P  :.  (none) 
E.  No  S  is  P  :.  All  S  is  not-P  :.  Some  not-P  is  S 
O.  Some  S  is  not  P  /   Some  S  is  7wt-P  :.  Some  not-P  is  S 
There  is  no  contrapositive  of  L,  because  the  obverse  of  L  is  in 
the  form  of  O.,  and  we  have  seen  that  O.  cannot  be  converted. 
O.,  however,  has  a  Contrapositive  {Some  not-P  is  S) ;  and  this 
is  sometimes  given   instead  of  the  converse,  and  called  the 
*  converse  by  negation.' 

Contraposition  needs  no  justification  by  the  Laws  of  Thought,  as  it  is 
nothing  but  a  compounding  of  Conversion  with  Obversion,  both  of 
which  processes  have  already  been  justified.  I  give  a  table  of  the  other 
ways  of  compounding  these  primary  modes  of  Immediate  Inference. 


k  (\' 


IMMEDIATE   INFERENCES 


77 


1 


In  this  table  a  and  b  stand  for  not- A  and  not-B,  and  had  better  be  read 
thus:  for  No  A  is  b,  No  A  is  not-B ;  for  All  b  is  a  (col.  6),  All  not-B  is 
not- A  ;  and  so  on. 

It  may  not,  at  first,  be  obvious  why  the  process  of  alternately  obvert- 
ing  and  converting  any  proposition  should  ever  come  to  an  end  ;  though 
it  will,  no  doubt,  be  considered  a  very  fortunate  circumstance  that  it 
always  does  end.  On  examining  the  results,  it  will  be  found  that  the 
cause  of  its  ending  is  the  inconvertibility  of  O.  For  E.,  when  obverted, 
becomes  A. ;  every  A.,  when  converted,  degenerates  into  I.;  every  I., 
when  obverted,  becomes  O. ;  O.  cannot  be  converted,  and  to  obvert  it 
again  is  merely  to  restore  the  former  proposition  :  so  that  the  whole 
process  moves  on  to  inevitable  dissolution.  I.  and  O.  are  exhausted  by 
three  transformations,  whilst  A.  and  E.  will  each  of  them  endure  seven. 

Except  Obversion,  Conversion  and  Contraposition,  it  has  not  been 
usual  to  bestow  special  names  on  these  processes  or  their  results.  But 
the  form  in  columns  7  and  10  [Some  a  is  B—Somc  a  is  not  B),  where  the 
original  predicate  is  affirmed  or  denied  of  the  contradictory  of  the 
original  subject,  has  been  thought  by  Dr.  Keynes  to  deserve  a  distinctive 
title,  and  he  has  called  it  the  Inverse.  Observe,  however,  that,  although 
the  Inverse  is  one  form.  Inversion  is  not  one  process,  but  is  obtained  by 
different  processes  from  E.  and  A.  respectively.  In  this  it  differs  from 
Obversion,  Conversion,  and  Contraposition,  each  of  which  stands  for 
one  process. 

The  Inverse  form  has  been  objected  to  on  the  ground  that  the  infer- 
ence All  A  is  B  .'.  Some  not- A  is  not  B,  distributes  B  (as  predicate  of  a 
negative  proposition),  though  it  was  given  as  undistributed  (as  predicate 
of  an  affirmative  proposition).  But  Dr.  Keynes  defends  it  on  the  ground 
that  (i)  it  is  obtained  by  Obversions  and  Conversions  which  are  a 
legitimate;  and  (2)  that  although  All  A  is  B  does  not  distribute  B  in 
relation  to  A,  it  does  distribute  B  in  relation  to  some  not-A  (namely,  in 
relation  to  whatever  not-A  is  not-B).  This  is  one  reason  why  in  stating 
the  rule  in  chap.  vi.  §  4, 1  have  written  ;  "  an  immediate  inference  ought 
to  contain  nothing  that  is  not  contained,  or  formally  implied,  in  the  pro- 
position from  which  it  is  inferred";  and  have  maintained  that  every 
term  formally  implies  its  contradictory. 

§  II.  Immediate  Inferences  from  Conditionals  are  those 
which  consist— (i)  in  changing  a  Disjunctive  into  a  Hypo- 
thetical, or  a  Hypothetical  into  a  Disjunctive,  or  either  into  a 
Categorical ;  and  (2)  in  the  relations  of  Opposition  and  the 
equivalences  of  Obversion,  Conversion,  and  secondary  or 
compound  processes,  which  we  have  already  examined  in 
respect  of  Categoricals.  As  no  new  principles  are  involved, 
it  may  suffice  to  exhibit  some  of  the  results. 


78       LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

^^^^:^l^!^^^^^  ^  ^^f-^-s  .ay  be  read  as 
i;  we  recognise  ^ourV^^lT^l:^^^^^^^ 

stand  to  one  another  in  a  Snn.r.  '7^^^^'''^^  ^-  '•  E.  O.,  these  plainly 
Thus  A.  and  E.  (7/^^/ C  '  n'^  Opposition,  just  as  Categoricals  do^ 
trades,  but  not  Comradictdes     s'in'^^  ''  ^'  ""  "  "''  ""^  ^'^  ^- 

tinges  be  D,  and  somet  Is  noO  thn  .  ^^  ^^  '^'''  ^^  ^^^  ^«-- 
And  if  they  are  both  fahe  the  I  S  ht  '''"'  '""""^  ^^^^  be  true, 
respectively  the  ContradtorilsTf  fh  'n  '"'' i  '"  '"'^  ^^"^'  '^^"^^ 
namely.  I.  of  E..  and  O  of  rBut  in^^  ^niversals  of  opposite  Quaht^ 
set   out   a  satisfactory  Itrfoo       '•''"' """^'""^^^^^^^^ 

(chap.  v.§  4).  the  forms  reSf^E^^^^^^^        '^^^"^^'   ^^   ^^  -- 
but  Exponibles.  ^  ^-  ^""^  O.  are  not  true  Disjunctives. 

The   Obverse,   Converse    anr?    r-     . 
exhibited  thus:  '         ^   ^ontrapositive  of  Hypotheticals   are 


\ 


Obverse. 
I/A  is  B,  C  is  not  d 

Sometimes  u-hen  A  is  B,  C  is  not  d 

UA  IS  B,  C  isd 

Sometimes  'when  A  is  B,  C  is  d 

CONTRAPOSITIVE. 

//  C  is  d,  A  is  not  B 

(none) 
Sometimes  u7ien  C  is  d,  A  ts  B 
Sometimes  u^hcn  C  is  d,  A  is  B 


Datum. 
A.  If  A  is  B.  CisD 
I.  Sometimes  K-/icn  A  is  B,  C  is  D 
^'  If  A  isB,C  isnotD 

^- ^^'^^times  K'/icn  A  is  B,C  is  not  D 

Converse. 
Sometimes  ichen  C  is  D,  A  is  B 
Sometimes  i^hen  C  is  D,  A  is  B 
If  C  is  D,  A  is  not  B 
(none) 

any  proposition  in  the  loL  A  7 euTsr      '''''''''■     ^""-  «'-" 
pos>t,o,>s  that  give  the  sense  of  Ob   "slf  r      '  '":  "^  ^'^'«  "^«  P™" 
Obve„«      ^  '"''''™°"' Conversion,  rt,-..  thus: 

CONVERSE._S»«rf/„>,.  „•,;„,  £  ;^ 
CONTRAPOSITIVF         \7../;  .,  "^   '^  ^  . 

For  a  Disjunctive  i         o^;  "'         "  '""  ^  ""'  ''''■ 

a  Disjunctive  in  the  form'  eiZTlsBlrT^ ^'''''''^'''''■^-     ^'-n 
Obverse-./„  ,„  ,ase  is  A  b.  and  C  at  tt  '  "'^  "^^^  '""^^  ^r  ils 

or  Contrapositive  of  such  a  DisL  t        """,  '""I  '^    ^"'  "°  Converse 
casting  It  into  the  Hypothetica^^rcregS  f:™  "^'''  "^"^^P'  ^^  «-' 


• 


CHAPTER  VIII 

ORDER   OF   TERMS,    EULER'S   DIAGRAMS,  LOGICAL 
EQUATIONS,    EXISTENTIAL   IMPORT   OF   PROPOSITIONS 

§  I.  Which  Term  is  the  Subject  and  which  the  Predicate  of  a  pro- 
position ?  In  most  of  the  exemplary  propositions  cited  by  Logicians 
it  will  be  found  that  the  subject  is  a  substantive  and  the  predicate  an 
adjective,  as  in  Men  aye  Mortal.  But,  in  literature,  sentences  in  which 
the  adjective  comes  first  are  not  uncommon,  as  Loud  n'as  the  applause, 
Dark  is  the  fate  of  man,  Great  is  the  glory  of  the  conquering  sword.  Here, 
then,  '  loud,'  '  dark  '  and  '  great '  occupy  the  place  of  the  Subject.  Are 
they  really  the  subject,  or  must  we  alter  the  order  of  such  sentences 
into  The  applause  was  loud,  etc.  ?  If  we  do,  and  then  proceed  to  convert, 
we  get  Loud  was  the  applause,  or  (more  scrupulously)  Some  loud  noise  was 
the  applause.  The  last  form,  it  is  true,  gives  the  subject  a  substantive 
word,  but  '  applause  '  has  become  the  predicate  ;  and  if  the  substantive 
'  noise'  was  not  implied  in  the  first  form,  Loud  is  the  applause,  by  what 
right  is  it  now  inserted  ?  The  recognition  of  Conversion,  in  fact,  re- 
quires us  to  admit  that,  in  a  logical  proposition,  the  term  preceding  the 
copula  is  subject  and  the  one  following  is  predicate.  And,  of  course, 
materially  considered,  the  mere  order  of  terms  in  a  proposition  can 
make  no  difference  in  the  method  of  proving  it,  nor  in  the  inferences 
that  can  be  drawn  from  it. 

Still,  if  the  question  is,  how  we  may  best  cast  a  literary  sentence  into 
logical  form,  good  grounds  for  a  definite  answer  may  perhaps  be  found. 
We  must  not  try  to  stand  upon  the  naturalness  of  expression,  for  Dark 
is  the  fate  of  man  is  quite  as  natural  as  Man  is  mortal.  When  the  pur- 
pose is  not  merely  to  state  a  fact,  but  also  to  express  our  feelings  about 
it.  to  place  the  grammatical  predicate  first  may  be  perfectly  natural 
and  most  effective.  But  the  grounds  of  a  logical  order  of  statement 
must  be  found  in  its  adaptation  to  the  purposes  of  proof  and  inference. 
Now  general  propositions  are  those  from  which  most  inferences  can  be 
drawn,  which,  therefore,  it  is  most  important  to  establish  if  true  ;  and 
they  are  also  the  easiest  to  disprove  if  false,  since  a  single  negative 
instance  suffices  to  establish   the  contradictory.      It  follows   that,  in 


8o        LOGIC:    DEDUCTIVE    AND   INDUCTIVE 

re-casting  a  literary  or  colloquial  sentence  for  logical  purposes,  we  should 
try  to  obtain  a  form  in  which  the  subject  is  distributed— is  either  a 
singular  term  or  a  general  term  predesignate  as  *  All '  or  '  No.'  Seeing, 
then,  that  most  adjectives  connote  a  single  attribute,  whilst  most  sub- 
stantives connote  more  than  one  attribute;  and  that  therefore  the 
denotation  of  adjectives  is  usually  wider  than  that  of  substantives ;  in 
any  proposition,  one  term  of  which  is  an  adjective  and  the  other  a 
substantive,  if  either  can  be  distributed  in  relation  to  the  other,  it  is 
nearly  sure  to  be  the  substantive ;  so  that  to  take  the  substantive  term 
for  Subject  is  our  best  chance  of  obtaining  an  universal  proposition. 
These  considerations  seem  to  justify  the  practice  of  Logicians  in  select- 
ing their  examples. 

For  similar  reasons,  if  both  terms  of  a  proposition  are  substantive, 
the  one  with  the  lesser  denotation  is  (at  least,  in  Affirmative  propositions) 
the  more  suitable  subject,  as  Cats  are  caynivores.  And  if  one  term  be 
abstract,  that  is  the  more  suitable  subject ;  for,  as  we  have  seen,  an 
abstract  term  may  be  interpreted  by  a  corresponding  concrete  one 
distributed,  as  Kindness  is  infectious;  that  is,  All  kind  actions  suggest 
imitation. 

If,  however,  a  controvertist  has  no  other  object  in  view  than  to  refute 
some  general  proposition  laid  down  by  an  opponent,  a  particular  pro- 
position is  all  that  he  need  disentangle  from  any  statement  that  serves 
his  purpose. 

§  2.  Toward  understanding  clearly  the  relations  of  the  terms  of  a 
proposition,  it  is  often  found  useful  to  employ  diagrams ;  and  the 
diagrams  most  in  use  are  the  circles  of  Euler. 

These  circles  represent  the  denotation  of  the  terms.  Suppose  the 
proposition  to  he  All  Jiollon'-Jwrncd  animals  ruminate:  then,  if  we  could 
collect  all  ruminants  upon  a  prairie,  and  enclose  them  with  a  circular 
palisade;  and  segregate  from  amongst  them  all  the  hollow-horned 
beasts,  and  enclose  them  with  another  ring-fence  inside  the  other ;  one 
way  of  interpreting  the  proposition  (namely,  in  denotation)  would  be 
figured  to  us  thus  : 

Fig.  I. 


An  Universal  Affirmative  may  also  state  a  relation  between  two  terms 
whose  denotation  is  co-extensive.     A  definition  always  does  this,  as 


Vn 


EULER'S    DIAGRAMS 


8i 


Man  is  a  rational  animal;  and  this,  of  course,  we  cannot  represent  by 
two  distinct  circles,  but  at  best  by  one  with  a  thick  circumference  to 
suggest  that  two  coincide,  thus  : 

Fig.  2. 


The  Particular  Affirmative  Proposition  may  be  represented  in  several 

ways.     In  the  first  place,  bearing  in  mind  that  '  Some  '  means  '  some  at 

least,  it  may  be  all,'  an  I.  proposition  may  be  represented  by  Figs,  i  and 

2  ;  for  it  is  true  that  Some  horned  animals  ruminate,  and  that  Some  men  are 

rational.     Secondly,  there  is  the  case  in  which  the  '  Some  things '  of 

which  a  predication  is  made  are,  in  fact,  not  all ;  whilst  the  predicate, 

though  not  given  as  distributed,  yet  might  be  so  given  if  we  wished  to 

state  the  whole  truth  ;  as  if  we  say  Some  men  aye  Chinese.     This  case  is 

also  represented  by  Fig.  i,  the  outside  circle  representing  'Men,'  and  the 

inside  one  '  Chinese. '    Thirdly,    .he  predicate  may  appertain'  to  some 

only  of  the  subject,  but  to  a  great  many  other  things,  as  in  Some  horned 

beasts  are  domestic;  for  it  is  true  that  some  are  not,  and  that  certain  other 

kinds  of  animals  are,  domestic.    This  case,  therefore,  must  be  illustrated 

by  overlapping  circles,  thus  : 

Fig.  3. 


HORNED 
ANIMALS 


DOMESTIC 
/ANIMALS 


The  Universal  Negative  is  sufficiently  represented  by  a  single  Fig.  (4^ 
two  circles  mutually  exclusive,  thus  : 


Fig.  4. 


That  is.  No  horned  beasts  are  carnivorous. 


82        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

Lastly,  the  Particular  Negative  may  be  represented  by  any  of  the 
Figs.  I,  3  and  4  ;  for  it  is  true  that  Some  ruminants  are  not  hollow-horned, 
that  Some  horned  animals  are  not  domestic,  ^nd  that  Some  horned  beasts  are 
not  carnivorous.  \^- 

Besides  their  use  in  illustrating  the  denotative  force  of  propositions, 
these  circles  may  also  be  used  to  verify  the  results  of  Obversion,  Con- 
version, and  the  secondary  modes  of  Immediate  Inference.  Thus  the 
Obverse  of  A.  is  clear  enough  on  glancing  at  Figs,  i  and  2  ;  for  if  we 
agree  that  whatever  term's  denotation  is  represented  by  a  given  circle,  the 
denotation  of  the  contradictory  term  shall  be  represented  by  the  space 
outside  that  circle;  then,  of  course,  if  it  is  true  that  All  holloiv-horned 
animals  are  ruminants,  it  is  at  the  same  time  true  that  No  hollow-horned 
animals  are  not-ruminants;  since  none  of  the  hollow-horned  are  found 
outside  the  palisade  that  encloses  the  ruminants.  The  Obverse  of 
I.,  E.,  or  O.  may  be  verified  in  a  similar  manner' 

As  to  the  Converse,  a  Definition  is  of  course  susceptible  of  Simple 
Conversion,  and  this  is  shown  by  Fig,  2  :  '  Men  are  rational  animals ' 
and  '  Rational  animals  are  men.'  But  any  other  A.  proposition  is  pre- 
sumably convertible  only  by  limitation,  and  this  is  shown  in  Fig.  i  ; 
where  All  hollow-horned  animals  are  ruminants,  but  we  can  only  say  that 
Some  ruminants  are  hollow-horned. 

That  I.  may  be  simply  converted  may  be  seen  in  Fig.  3,  which  repre- 
sents the  least  that  an  I.  proposition  can  mean  ;  and  that  E.  may 
be  simply  converted  is  manifest  in  Fig.  4. 

As  for  O.,  we  know  that  it  cannot  be  con\erted,  and  this  is  made  plain 
enoug'i  by  glancing  at  Fig.  i  ;  for  that  represents  theO.,  Some  ruminants 
are  not  holloji'-horned,  but  also  shows  this  to  be  compatible  with  All 
hollow  horned  animals  are  ruminants  (A.).  Now  in  Conversion  there  is  (by 
definition)  no  change  of  quality.  The  Converse,  then,  of  Some  ruminants 
are  not  hollow-horned  must  be  a  negative  proposition,  having  'hollow- 
horned'  for  its  subject,  either  in  E.  or  O.  ;  but  there  would  be  re- 
spectively the  Contrary  and  Contradictory  of  ^//  hollow-horned  animals 
are  ruminants;  and,  therefore,  if  this  is  true,  they  must  both  be  false. 

But  (referring  still  to  Fig.  i)  the  legitimacy  of  contrapositing  O. 
is  equally  clear ;  for  if  Some  ruminants  are  not  hollow-horned.  Some  animals 
that  are  not  holloiv-horned  are  ruminants,  namely,  all  the  animals  between 
the  two  ring-fences.  Similar  inferences  may  be  illustrated  from  Figs.  3 
and  4.  And  the  Contraposition  of  A.  may  be  verified  by  Figs,  i  and  2, 
and  the  contrapositive  of  E.  by  Fig.  4. 

Lastly,  the  Inverse  of  A.  is  plain  from  Fig.  i—Some  things  that  are  not 
hollow-horned  are  not  ruminants^  namely,  all  things  that  lie  outside  the 
outer  circle  and  are  neither  '  ruminants  '  nor  '  hollow-horned. '  And  the 
Inverse  of  E.  may  be  studied  in  Fig.  4— Some  things  that  are  not-Jiorned 
beasts  are  carnivorous. 

Notwithstanding  the  facility  and  elegance  of  the  demonstrations  thus 


LOGICAL   EQUATIONS 


83 


^ 


obtained,  there  is  much  to  be  said  for  the  opinion  that  such  a  dia- 
grammatic method  is  not  properly  logical.     It  seems  to  be  agreed  that 
fundamentally  the  relation  asserted   (or  denied)  to  exist  between  the 
terms  of  a  proposition,  is  a  relation  between  the  terms  as  determined  by 
their  attributes  or  connotation ;    whether  we  take  Mill's  view,  that  a 
proposition  asserts  that  the  connotation  of  the  subject  is  a  mark  of  the 
connotation  of  the  predicate  ;  or  Dr.  Venn's  view,  that  things  denoted  by 
the  subject  (as  having  its  connotation)  have  (or  have  not)  the  attribute 
connoted  by  the  predicate  ;  or,  the  Conceptualist  view,  that  a  judgment 
is  a  relation  of  concepts  (that  is,  of  connotations).     At  any  rate,  it  is 
certain  that,  with  a  few  artificially  framed  exceptions  (such  as  '  kings 
now  reigning  in  Europe  '),  the  denotation  of  a  term  is  never  directty 
known,  but  consists  merely  in  'all  things  that  have  the  connotation.' 
And  I  venture  to  think  that  the  value  of  logical  training  depends  very 
much  upon  our  habituating  ourselves  to  construe  propositions,  and  to 
realise  the  force  of  inferences  from  them,  according  to  the  connotation 
of  their  terms ;  and  that,  therefore,  a  student  does  well  not  to  turn  too 
hastily  to  the  circles,  but  rather  to  regard  them  as  a  means  of  verifying 
in  denotation  the  conclusions  that  he  has  already  learnt  to  recognise  as 
necessary  in  connotation.     (Keynes  :  Formal  Logic,  Part  II.  c.  4.) 

§  3.  The  equational   treatment   of  propositions   is   closely 
connected  with   the  diagrammatic.      Hamilton  thought  it   a 
great    merit   of  his   plan    of  quantifying   the   predicate,    that 
thereby  every  proposition  is   reduced  to    its    true    form— an 
equation.     According  to  this  doctrine,  the  proposition  A/i  X 
is  all  K(U.)  equates  X  and  Y;  the  proposition  All  X  is  some 
F(A.)  equates  X  with  some  part  of  Y;  and  similarly  with  the 
other  affirmatives  (Y.  and  I.).     And  so  far  it  is  easy  to  follow 
his  meaning:  the  Xs  are  identical  with  some  or  all   the  Ys. 
But,  coming  to   the  negatives,   the  equational  interpretation 
is  certainly  less  obvious.     The  proposition  No  X  is    V  (E.) 
cannot  be  said  in  any  sense  to  equate  X  and  Y ;  though,  if  we 
obvert  it  into  All  X  is  some  not-  F,  we  have  (in  the  same  sense, 
of  course,  as  the  above  affirmative  forms)  X  equated  with  part 
at  least  of  '  not-Y.' 

But  what  is  this  sense?  Clearly  not  the  same  as  that  in 
which  Mathematical  terms  are  equated,  namely,  in  respect  of 
some  mode  of  quantity.  For  if  we  may  say  Some  X  is  some  Y, 
these  Xs  that  are  also  Ys  are  not  merely  the  same  in  number, 


84        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

or  position,  or  figure,  or  other  determination  of  space;  they 
are  the  same  in  every  respect,  both  quantitative  and  quali- 
tative, are  in  fact  identical.     The  proposition  2  +  2-4  means 
that  any  two  things  added  to  any.  other  two  are,  in  respect  of 
number,  equal  to  any  three  things  added  to  one  other ;  and 
this  is  true  of  all  things  that  can  be  counted,  however  much 
they  may  differ  in  other  ways.     But  A/I  X  is  all  F means  that 
Xs  and  Ys  are  the  same  things,  although  they  have  different 
names  when  viewed  in  different  aspects  or  relations.     Thus 
all  equilateral  triangles  are  equiangular  triangles ;  but  in  one 
case  they  are  named  from  the  equality  of  their  angles  and  in 
the  other  from  the  equality  of  their  sides.     Similarly,  'British 
subjects  '  and  '  subjects  of  Queen  Victoria  '  are  the  same  people, 
named  in  one  case  from  the  person  of  the  Crown,  and  in  the 
other  from  the  Imperial  Government.  These  Logical  equations, 
then,  are  in  truth  identities  of  denotation  ;  and  they  are  fully 
illustrated  by  the  relations  of  circles  described  in  the  previous 
section. 

When  we  are  told  that  logical  propositions  are  to  be  consi- 
dered as  equations,  we  naturally  expect  to  be  shown  some 
interesting  developments  of  method  in  analogy  with  the 
equations  of  Mathematics ;  but  from  Hamilton's  innovations 
no  such  thing  results.  This  cannot  be  said,  however,  of  the 
equations  of  Symbolic  Logic ;  which  are  the  starting-point  of 
very  remarkable  processes  of  ratiocination.  As  the  subject 
of  Symbolic  Logic,  as  a  whole,  lies  beyond  the  compass  of 
an  ordinary  manual,  it  will  be  enough  to  give  Dr.  Venn's 
equations  corresponding  with  the  four  propositional  forms  of 
common  Logic. 

According  to  this  system,  universal  propositions  are  to  be 
regarded  as  not  necessarily  implying  the  existence  of  their 
terms ;  and  therefore,  instead  of  giving  them  a  positive  form, 
they  are  translated  into  symbols  that  express  what  they  deny.' 
For  example,  the  proposition  All  devils  are  ugly  need  not 
imply  that  any  such  things  as  Mevils '  really  exist;  but  it 
rertainly  does  imply  that  D.nnls  that  are  not-ugly  do  not  exist. 


LOGICAL   EQUATIONS 


85 


I 


Similarly,  the  proposition  No  angels  are  ugly  implies  that 
Angels  that  are  ugly  do  not  exist.  Therefore,  writing  x  for 
'devils,'  y  for  '  ugly,'  and  y  for  '  not-ugly,'  we  may  express  A., 
the  universal  affirmative,  thus  : 

A.  x7  =  o. 
That  is,  X  that  is  not y  is  nothing;  or.  Devils  that  are  not  ugly 
do  not  exist.     And,  similarly,  writing  x  for  'angels  '  and  y  for 
'  ugly,'  we  may  express  E.,  the  universal  negative,  thus : 

E.  xy  =  o. 

That  is,  x  that  is y  is  nothing;  or.  Angels  that  are  ugly  do  not 
exist. 

On  the  other  hand,  particular  propositions  are  regarded  as 
implying  the  existence  of  their  terms,  and  the  corresponding 
equations  are  so  framed  as  to  express  existence.  With  this 
end  in  view,  the  symbol  v  is  adopted  to  represent  '  something ', 
or  indeterminate  reality,  or  more  than  nothing.  Then,  taking 
any  particular  affirmative,  such  as  Some  metaphysicians  are 
obscure,  and  writing  x  for  '  metaphysicians ',  and  y  for  ' obscure', 
we  may  express  it  thus  : 

I.  xy  =  v. 
That  is,  .V  that  is  y  is  something;  or.  Metaphysicians  that  are 
obscure  do  occur  in  experience  (however  few  they  may  be,  or 
whether  they  be  all  obscure).  And,  similarly,  taking  any 
particular  negative,  such  as  Some  giants  are  not  cruel,  and 
writing  X  for  '  giants  '  and  7  for  '  not-cruel ',  we  may  express  it 
thus : 

O.  xy  =  v. 
That  is,  .r  that  is  not y  is  something;  or,  giants  that  are  not  cruel 
do  occur— m  romances,  if  nowhere  else. 

Clearly,  these  equations,  like  those  of  Hamilton,  are 
concerned  with  denotation.  A.  and  E.  affirm  that  the  'com- 
pound terms  xy  and  xy  have  no  denotation ;  and  I.  and  O. 
declare  that  xy  and  xy  have  denotation,  or  stand  for  something! 
Here,  however,  the  resemblance  to  Hamilton's  system  ceases ; 
for  the  Symbolic  Logic,  by  operating  upon  more  than  twj 
terms   simultaneously,    by   adopting    the    algebraic    signs    of 


"4*-««| 


I 


S6 


LOGIC:   DEDUCTIVE   AND  INDUCTIVE 


operation,  +,  _,  x,  -^  (with  a  special  signification),  and 
manipulating  the  symbols  by  quasi-algebraic  processes,  obtains 
results  which  the  common  Logic  reaches  (if  at  all)  with  much 
greater  difficulty.  If,  indeed,  the  value  of  logical  systems  were 
to  be  judged  of  by  the  results^  obtainable,  formal  deductive 
Logic  would  probably  be  superseded.  And,  as  a  mental 
discipline,  there  is  much  to  be  said  in  favour  of  the  symbolic 
method.  But,  as  an  introduction  to  philosophy,  the  common 
Logic  must  hold  its  ground.     (Venn's  SymM'^  Logic,  c.  7.) 

§  4.  Whether  Formal  Logic  involves  any  general  assump- 
tion as  to  the  real  existence  of  the  terms  of  propositions,  is  a 
question  that  has  lately  excited  some  interest ;  so  that  a  few 
remarks  upon  it  will  be  expected  here.  But,  as  it  is  too 
abstruse  a  matter  to  be  fully  discussed  in  a  manual,  if  my 
treatment  of  it  seem  somewhat  dogmatic,  the  need  of  brevity 
must  be  my  excuse. 

I  observe,  then,  in  the  first  place,  that  Logic  treats  primarily 
of  the  relations  implied  in  propositions.     This  follows  from  its 
being  the  science  of  proof  for  all  sorts  of  (qualitative)  proposi- 
tions; since  all  sorts  of  propositions  have  nothing  in  common 
except  the  relations  they  imply.     But,  secondly,  relations  with- 
out terms  of  some  sort  are  not  to  be  thought  of;  and.  hence 
even  the  most  formal  illustrations  of  logical  doctrine  comprise 
such  terms  as  S  and  P,  X  and  Y,  or  x  and  y,  in  a  symbolic 
or   representative  character.     Terms,  therefore,  of  some  sort 
are  assumed  to  exist  (together  with  their  negatives  or  contra- 
dictories) >/-  the  purposes  of  logical  manipulation. 

Thirdly,  however,  that  Formal  Logic  cannot  directly  involve 
the  existence  of  any  particular  concrete  terms,  such  as  '  man ' 
or  '  mountain,'  is  implied  in  the  word  '  formal,'  that  is,  '  con- 
fined to  what  is  common  or  abstract ' ;  since  the  only  thing 
common  to  all  terms  is  to  be  related  in  some  way  to  other 
terms.  The  actual  existence  of  any  concrete  thing  can  only  be 
known  by  experience,  as  with  '  man  '  or  '  mountain '  •  or  by 
methodically  justifiable  inference  from  experience,  as  with 
*  atom  '  or  *  ether.' 


^ 


EXISTENTIAL  IMPORT  87 

Nevertheless,  fourthly,  the  existence  or  non-existence  of  par- 
ticular terms  may  come  to  be  implied,  namely,  wherever  the 
very  fact  of  existence,  or  of  some  condition  of  existence,  is  an 
hypothesis  or  datum.  Thus,  given  the  proposition  All  S  is  P, 
to  be  P  IS  made  a  condition  of  the  existence  of  S ;  whence  it 
follows  that  an  S  that  is  not  P  does  not  exist  (xy  =  o).  On  the 
further  hypothesis  that  S  exists,  it  follows  that  P  exists.  On 
the  hypothesis  that  S  does  not  exist,  the  existence  of  P  is 
problematic ;  but,  then,  if  P  does  exist  we  cannot  convert  the 
proposition  ;  since  Some  P  is  S  (P  existing)  would  involve  the 
existence  of  S  ;  which  is  contrary  to  the  hypothesis. 

Assuming  that  Universals  do  not,  whilst  Particulars  do,  imply 
the  existence  of  their  subjects,  we  cannot  infer  the  subalternate 
(I.  or  O.)  from  the  subalternans  (A.  or  E.),  for  that  is  to  ground 
the  actual  on  the  problematic ;  and  for  the  same  reason  we 
cannot  convert  A.  per  accidens. 

Assuming,  again,  a  certain  suppositio  or  universe,  to  which 
in  a  given  discussion  every  argument  shall  refer,  then,  any  pro- 
positions whose  terms  lie  outside  that  suppositio  are  irrelevant, 
and  for  the  purposes  of  that  discussion  may  be  called  false.' 
Thus  propositions,  which  according  to  the  doctrine  of  Opposi- 
tion appear  to  be  Contradictories,  may  then  cease  to  be  so  ; 
for  of  Contradictories  one  is  true  and  the  other  false ,  but,  in 
the  case  supposed,  both  are  technically  false.      If  the   sub- 
ject of  discussion  is  Zoology,  all  propositions  about  Centaurs 
or  Unicorns  are  absurd  ;  and  such  specious  Contradictories  as 
No  Centaurs  play  the  lyre—Some  Cetitaurs  do  play  the  lyre;  or 
All  unicor?is  fight  ivith  lions—Some  Unicorns  do  not  fight  with 
lions,  are  both  false  or  meaningless,  because  in  Zoology  there  are 
no  Centaurs  nor  Unicorns  ;  and,  therefore,  in  this  reference, 
the  propositions  are  not  really  contradictory.    But  if  the  subject 
of  discussion  or  suppositio  be  Mythology  or  Heraldry,   such 
propositions    as    the  above    are    to    the  purpose,   and    form 
legitimate  pairs  of  Contradictories. 

In  Formal  Logic,  in  short,  we  may  make  at  discretion  any 
assumption  whatever  as  to  the  existence,  or  as  to  any  condition 


88 


LOGIC:   DEDUCTIVE  AND   INDUCTIVE 


of  the  existence  of  any  term  or  terms  ;  and  then  certain  impli- 
cations and  conclusions  follow  in  consistency  with  that  hypo- 
thesis or  datum.  Still,  our  conclusions  will  themselves  be  only 
hypothetical,  depending  on  the  truth  of  the  datum  ;  and,  of 
course,  until  that  is  empirically  ascertained,  we  are  as  far  as 
ever  from  empirical  reality.  (Venn :  Symbolic  Logic,  c.  6 ; 
Keynes:  Formal  Logic,  Part  II.  c.  7.) 


CHAPTER  IX 
FORMAL  CONDITIONS  OF  MEDIATE  INFERENCE 

§  I.  A  Mediate  Inference  is  a  proposition  that  depends  for 
proof  upon  two  or  more  other  propositions,  so  connected  together 
by  one  or  more  terms  (which  the  evidentiary  propositions,  or 
each  pair  of  them,  have  in  common)  as  to  justify  a  certain 
conclusion,  namely,  the  proposition  in  question.  The  type  o. 
(more  properly)  the  unit  of  all  such  modes  of  proof,  when  of  a 
strictly  logical  kind,  is  the  Syllogism,  to  which  We  shall  see 
that  all  other  modes  are  reducible.  It  may  be  exhibited 
symbolically  thus  : 

M  is  P ; 
S  is  M  : 
..    Sis  P. 
Syllogisms  may  be  classified,  as  to  quantity,  into  Universal 
or  Particular,  according  to  the  quantity  of  the  conclusion  ;  as 
to   quality,  into    Attirmative   or   Negative,   according   to   the 
quality  of  the  conclusion ;  and,  as  to  relation,  into  Categorical, 
Hypothetical  and  Disjunctive,  according  as  all  their  proposi- 
tions are  categorical,  or  one  (at  least)  of  their  evidentiary  pro- 
positions is  a  hypothetical  or  a  disjunctive. 

We  will  begin  with  Categorical   Syllogisms,  of  which  the 
following  is  a  concrete  example  : 

All  authors  are  vain  ; 
Cicero  is  an  author  : 
.".    Cicero  is  vain. 
Here    e  may  suppose  that  there  are  no  direct  means  of  know- 
ing that  Cicero  is  vain ;  but  we  happen  to  know  that  all  authors 


90        LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

are  vain  and  that  he  is  an  author  ;  and  these  two  propositions 
put    together  unmistakably  imply  that  he  is  vain.      In  other 
words,  we  do  not  at  first  know  any  relation  between  *  Cicero ' 
and  '  vanity ' ;  but  we  know  that  these  two  terms  are  severally 
related  to  a  third  term,  'author,'  hence  called  a  Middle  Term; 
and  thus  we  perceive,  by  mediate  evidence,  that  they  are  re- 
lated to  one  another.     This  sort  of  proof  bears  an  obvious  re- 
semblance to  the  mathematical  proof  of  equality  between  two 
quantities,  that  cannot  be  directly  compared,  by  showing  the 
equality  of  each  of  them  to  some  third  quantity:  A  =  B  =  C 
•'•  A  =  C.     Here  B  is  a  middle  term. 

We  have  to  inquire,  then,  what  conditions  must  be  satisfied 
in  order  that  a  Syllogism  may  be  formally  conclusive  or  valid. 
An  apparent  Syllogism  that  is  not  really  valid  is  called  a 
Parasyllogism. 

§  2.  General  Canons  of  the  Syllogism. 

(i)  A  Syllogism  contains  three,  and  no  more,  distinct   pro- 
positions. 

(2)  A  Syllogism  contains  three,  and  no  more,  distinct  uni- 
vocal  terms. 


These  two  Canons  imply  one  another.      Three  propositions  with  less 
than  three  terms  could  only  be  connected  in  some  of  the  modes  of 
Immediate  Inference.      Three  propositions  with  more  than  three  terms 
do  not  show  that  connection  of  two  terms  by  means  of  a  third,  which  is 
the  desideratum  for  proving  a  Mediate  Inference.     If  we  write- 
All  authors  are  vain  ; 
Cicero  is  a  statesman  ; 
there  are  four  terms  and  no  Middle  Term,  and  therefore  there  is  no  proof 
Ur  if  we  write —  ^ 

All  authors  are  vain  ; 

Cicero  is  an  author ; 
.'.  Cicero  is  a  statesman  ; 
here  the  term  •  statesman '  occurs  without  any  voucher;  it  appears  in 
the  inference  but  not  in  the  evidence,  and  therefore  violates  the  maxim 
of  all  formal  proof.  •  not  to  go  beyond  the  evidence  '  (chap,  vi  S  4)      it 
IS  true  that  if  any  one  argued—  •  b  ^/.     ai 

All  authors  are  vain  ; 
Cicero  wrote  on  philosophy  ; 
.•.  Cicero  is  vain  : 


CONDITIONS   OF   MEDIATE   INFERENCE       91 

this  could  not  be  called  a  bad  argument  or  a  material  fallacy  ;  but  it 
would  be  a  needless  departure  from  the  form  of  expression  in  which  the 
connection  between  the  evidence  and  the  inference  is  most  easily  seen  • 
It  would  generally  be  called  a  formal  fallacy. 

Still  a  mere  adherence  to  the  same  form  of  words  in  the  expression  of 
terms  is  not  enough  :  we  must  also  attend  to  their  meaning.  For  if  the 
same  word  be  used  ambiguously  (as  'author'  now  for  '  father  '  and 
anon  for  '  man  of  letters ')  it  becomes  as  to  its  meaning  two  terms ;  so 
that  we  have  four  in  all.  Then,  if  the  ambiguous  term  be  the  Middle, 
no  connection  is  shown  between  the  other  two ;  if  either  of  the  others 
be  ambiguous,  something  seems  to  be  inferred  which  has  never  been 
really  given  in  evidence. 

The  above  two  Canons  are,  indeed,  involved  in  the  definition 
of  a  Categorical  Syllogism,  which  may  be  thus  stated  :  A  Cate- 
gorical Syllogism  is  a  form  of  proof  or  reasoning  (way  of  giving 
reasons)  in  which  one  categorical  proposition  is  established  by 
comparing  two  others  that  contain  together  only  three  terms,  or 
that  have  one  and  only  one  term  in  common. 

The  proposition  established,  derived,  or  inferred,  is  called 
the  Conclusion  :  the  evidentiary  propositions  by  which  it  is 
proved  are  called  the  Premises. 

The  term  common  to  the  Premises,  by  means  of  which  the 
other  terms  are  compared  is  called  the  Middle  Term.  For 
the  other  Terms,  the  Subject  of  the  Conclusion  is  called 
the  Minor  Term ;  the  Predicate  of  the  Conclusion,  the  Major 
Term. 

The  Premise  in  which  the  minor  term  occurs  is  called  the 
Minor  Premise ;  that  in  which  the  major  term  occurs  is  called 
the  Major  Premise.      And  a  Syllogism  is  usually  written  thus  : 

Major  Premise— All  Authors  (Middle)  are  vain  (Major) ; 

Minor  Premise— Cicero  (Minor)  is  an  author  (Middle) : ' 

Conclusion—.-.  Cicero  (Minor)  is  vain  (Major). 
Here  we  have  three  propositions  with  three  terms,  each  term 
occurring  twice.  The  Minor  and  Major  terms  are  so  called, 
because  when  the  conclusion  is  an  universal  affirmative  (which 
only  occurs  in  Barbara;  see  chap.  x.  §  6),  its  subject  and 
predicate  are  respectively  the  less  and  the  greater  in  extent  or 
denotation.     It  should  be  carefully  noticed  that  the  premises 


92        LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

are  called  after  the  peculiar  terms  they  contain  :  the  expressions 
*  Major  Premise'  and  'Minor  Premise'  have  nothing  to  do 
with  the  order  in  which  the  premises  are  presented ;  though 
it  is  usual  to  place  the  Major  tirst. 

(3)  No  term  must  be  distributed  in  the  conclusion  unless  it 
is  distributed  in  the  premises. 

It  is  usual  to  give  this  as  one  of  the  General  Canons  of  the  Syllogism  ; 
but  we  have  seen  (chap.  vi.  §  6)  that  it  is  of  wider  application.  Indeed, 
'not  to  go  beyond  the  evidence'  belongs  to  the  definition  of  formal 
proof.  A  breech  of  this  rule  in  a  Syllogism  is  the  fallacy  of  Illicit 
Process  of  the  Minor,  or  of  the  Major,  according  to  which  term 
has  been  unwarrantably  distributed.  The  following  parasyllogism 
illicitly  distributes  both  terms  of  the  conclusion  : 

All  poets  are  pathetic  ; 

Some  orators  are  not  poets ; 
.•.  No  orators  are  pathetic. 

(4)  The  Middle  Term  must  be  distributed  at  least  once  in 
the  premises. 

For  the  use  of  mediate  evidence  is  to  show  the  relation  of  terms  that 
cannot  be  directly  compared  ;  this  is  only  possible  if  the  Middle  term 
furnishes  the  ground  of  comparison  ;  and  this  (in  Logic)  requires  that 
the  whole  denotation  of  the  Middle  should  be  either  included  or 
excluded  by  one  of  the  others ;  since  if  we  only  know  that  the  other 
terms  are  related  to  some  of  the  Middle,  their  respective  relations  may 
not  be  with  the  same  part  of  it.  Indeed,  if  the  Middle  is  undistributed 
in  both  premises,  Whately  regards  it  as  ambiguous ;  in  which  case  the 
pretended  syllogism  depending  on  it  has  four  terms  :  so  that  this  4th 
Canon  may  be  regarded  as  reducible  to  the  2nd. 

It  is  true  that  in  what  has  been  strangely  called  the  "numerically 
definite  syllogism,"  an  inference  may  be  drawn,  though  our  canon  seems 
to  be  violated.     Thus  : 

60  sheep  in  100  are  horned  ; 

60  sheep  in  100  are  black  faced  ; 
.*.  at  least  20  blackfaced  sheep  in  100  are  horned. 
But  such  an  argument,  though  I  presume  it  may  be  correct  Arithmetic, 
is  not  Logic  at  all ;  and  when  such  numerical  evidence  is  obtainable 
the  comparatively  indefinite  arguments  of  Logic  are  needless.    Another 
apparent  exception  more  to  the  purpose  is  the  following : 

Most  men  are  5  feet  high ; 

Most  men  are  semi-rational : 
.*.  Some  semi-rational  things  are  5  feet  high. 
Here  the  Middle  Term  (men)  is  distributed  in  neither  premise,  yet  the 


I 


CONDITIONS   OF   MEDIATE   INFERENCE       93 

indisputable  conclusion  is  a  logical  proposition.  Observe,  however,  that 
the  premises  are  really  arithmetical ;  for  '  most '  means  '  more  than 
half,'  or  more  than  50  per  cent. 

For  Mediate  Inference  depending  on  truly  logical  premises,  then,  it  is 
necessary  that  one  premise  should  distribute  the  Middle  Term  ;  and  the 
reason  of  this  may  be  illustrated  even  by  the  above  supposed  ex- 
ceptions. For  in  them  the  premises  are  such  that,  though  neither  premise 
by  itself  distributes  the  Middle,  yet  they  always  do  so  between  them, 
and  that  with  a  certain  surplus.  For  if  each  premise  dealt  with  exactly 
half  the  Middle.,  thus  barely  distributing  it  between  them,  there  would 
be  no  logical  proposition  inferrible  (though,  of  course,  there  might  be  a 
conclusion  of  numerical  probability).  We  require  that  the  Middle  as 
used  in  one  premise,  should  necessarily  overlap  the  Middle  as  used  in 
the  other,  so  as  to  furnish  common  ground  for  comparing  the  other 
terms.  Hence  I  have  defined  the  Middle  as  '  that  Term  common 
to  both  premises  by  means  of  which  the  other  terms  are  compared.' 

(5)  One  at  least  of  the  premises  must  be  affirmative  ;  or, 
from  two  negative  premises  nothing  can  be  inferred. 

The  fourth  Canon  required  that  the  Middle  term  should  be  given  us 
distributed,  or  in  its  whole  extent,  in  order  to  afford  sure  ground  of 
comparison  for  the  others.  But  that  such  comparison  may  be  effected, 
something  more  is  requisite ;  the  relation  of  the  other  terms  to  the 
Middle  must  be  of  a  certain  character.  One  at  least  of  them  must  be, 
as  to  its  extent  or  denotation,  partially  or  wholly  identified  with  the 
Middle;  so  that  to  that  extent  it  may  be  known  to  bear  to  the  other 
term,  whatever  relation  we  are  told  that  so  much  of  the  Middle  bears 
to  that  other  term.  Now,  identity  of  denotation  can  only  be  predicated 
in  an  affirmative  proposition  :  one  premise,  then,  must  be  affirmative. 

If,  however,  both  premises  are  negative,  we  only  know  that  both 
the  other  terms  are  partly  or  wholly  excluded  from  the  Middle,  or  are 
not  identical  with  it  in  denotation :  where  they  lie,  then,  in  relation  to 
one  another,  we  have  no  means  of  knowing.  Similarly,  in  the  mediate 
comparison  of  quantities,  if  we  are  told  that  A  and  C  are  both  of  them 
unequal  to  B,  we  can  infer  nothing  as  to  the  relation  of  C  to  A.  Hence 
the  premises — 

No  electors  are  sober ; 
No  electors  are  independent, 
howe'ver  suggestive,  do  not  formally  justify  us  in  inferring  any  connec- 
tion between  sobriety  and  independence.    F'ormally  to  draw  a  conclusion, 
we  must  have  affirmative  grounds,  such  as  in  this  case  we  may  obtain 
by  obverting  both  premises : 

All  electors  are  not-sober ; 
All  electors  are  not-independent ; 
-\  Some  who  are  not-independent  are  not-sober. 


II 


I 


94 


LOGIC:   DEDUCTIVE   AND    INDUCTIVE 


(6)  (a)  If  one  premise  is  negative,  the  conclusion  must  be 
negative :  and  (<^)  to  prove  a  negative  conclusion,  one  premise 
must  be  negative. 

(a)  For  we  have  seen  that  one  premise  must  be  affirmative,  and  that 
thus  one  term  must  be  partly  (at  least)  identified  with  the  Middle.  If 
then  the  other  premise,  being  negative,  predicates  the  exclusion  of  the 
other  term  from  the  Middle,  this  other  term  must  be  excluded  from  the 
first  term,  so  far  as  we  know  the  first  to  be  identical  with  the  Middle  : 
and  this  exclusion  will  be  expressed  by  a  negative  conclusion.  The 
analogy  of  the  mediate  comparison  of  quantities  may  here  again  be 
noticed  :  if  A  is  equal  to  B,  and  B  is  unequal  to  C,  A  is  unequal  to  C. 

{b)  If  both  premises  are  affirmative,  the  relations  of  both  terms  to 
the  Middle  are  more  or  less  inclusive,  and  therefore  furnish  no  ground 
for  an  exclusive  inference.  This  also  follows  from  the  function  of  the 
Middle  term. 

For  the  more  convenient  application  of  these  canons  to  the 
testing  of  syllogisms,  it  is  usual  to  derive  from  them  three 
Corollaries  : 

(i)  Two  particular  premises  yield  no  conclusion. 

For  if  both  premises  are  affirmative  all  their  terms  are  undistributed, 
the  subjects  by  predesignation,  the  predicates  by  position  (chap.  v.  §  i) ; 
and  therefore  the  Middle  must  be  undistributed,  and  there  can  be  no 
conclusion. 

If  one  premise  is  negative,  its  predicate  is  distributed  by  position : 
the  other  terms  remaining  undistributed.  But,  by  Canon  6,  the  conclu- 
sion (if  any  be  possible)  must  be  negative  ;  and  therefore  its  predicate, 
the  Major  term,  will  be  distributed.  In  the  premises,  therefore,  both  the 
Middle  and  the  Major  terms  should  be  distributed,  which  is  impos- 
sible :  e.g., 

Some  M  is  not  P ; 

Some  S  is  M  ; 
.'.  Some  S  is  not  P. 
Here,  indeed,  the  Major  term  is  legitimately  distributed  (though  the 
negative  premise  might  have  been  the  Minor) ;  but  M,  the. Middle  term, 
is  distributed  in  neither  premise,  and  therefore  there  can  be  no  con- 
clusion. 

(ii)  If  one  premise  is  particular,  so  is  the  conclusion. 

For,  again,  if  both  premises  are  affirmative,  they  only  distribute  one 
term,  the  subject  of  the  Universal  premise,  and  this  must  be  the  Middle 
term.  The  Minor  term,  therefore,  is  undistributed,  and  the  conclusion 
roust  be  particular. 


CONDITIONS   OF   MEDIATE   INFERENCE      95 

If  one  premise  is  negative,  the  two  premises  together  can  distribute 
only  two  terms,  the  subject  of  the  Universal  and  the  predicate  of  the 
negative  (which  may  be  the  same  premise).  One  of  these  terms  must 
be  the  Middle ;  the  other  (since  the  conclusion  is  negati\'e)  must  be  the 
Major.  The  Minor  term,  therefore,  is  undistributed,  and  the  conclusion 
must  be  particular. 

(iii)  From  a  particular  Major  and  a  negative  Minor  premise, 
nothing  can  be  inferred. 

For  the  Minor  premise  being  negative,  the  Major  premise  must  be 
affirmative  (5th  Canon) ;  and  therefore,  being  particular,  distributes 
the  Major  term  neither  in  its  subject  nor  in  its  predicate.  But  since 
the  conclusion  must  be  negative  (6th  Canon),  a  distributed  Major  term 
is  demanded:  e.g.,  /fif^i 

Some  M  is  P ;  T  y 

No  S  is  M  ;  ^^ 


Here  the  Minor  and  the  Middle  terms  are  both  distributed,  but  not  the 
Major  (P) ;  and,  therefore,  a  negative  conclusion  is  impossible. 

§  3.  First  Principle  or  Axiom  of  the  Syllogism. — Hitherto 
in  this  chapter  we  have  been  analysing  the  conditions  of  valid 
mediate  inference.  We  have  seen  that  a  single  step  of  such 
inference,  a  Syllogism,  contains  when  fully  expressed  in  lan- 
guage three  propositions  and  three  terms,  and  that  these  terms 
must  stand  to  one  another  in  the  relations  required  by  the 
fourth,  fifth,  and  sixth  Canons.  We  now  come  to  a  principle 
which  conveniently  sums  up  these  conditions ;  it  is  called  the 
Dictum  de  om?ii  et  nullo^  and  may  be  stated  thus  : 

Whatever  is  predicated  (affirmatively  or  negatively)  of  a 
Term  distributed, 

In  which  Term  another  is  given  as  (partly  or  wholly)  in- 
cluded, 

May  be  predicated  in  like  manner  of  (part  or  all  of)  the 
latter  Term. 
Thus  stated  (nearly  as  by  Whately  in  die  introduction  to  his 
Logic)  the  Dictum  follows  line  by  line  the  course  of  a  Syllogism 
in  the  First  Figure  (see  chap.  x.  §  2).  To  return  to  our  former 
example  :  All  authors  are  vain  is  the  same  as — Vanity  is  pre- 
dicated of  all  authors ;  Cicero  is  an  author  is  the  same  as— 


i 


%*..H| 


96       LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

Cicero  is  included  amongst  authors :  therefore, OV^z-^/V  vain.ox — 
Vanity  may  be  predicated  of  Cicero.  The  Dictuvi  then  requires  : 
(i)  three  propositions;  (2)  three  terms;  (3)  that  the  Middle 
be  distributed  ;  (4)  that  one  premise  be  affirmative,  since  only 
by  an  affirmative  proposition  can  one  term  be  given  as  included 
in  another;  (5)  that  if  one  premise  is  negative  the  conclusion 
be  so  too,  since  whatever  is  predicated  of  the  Middle  is  predi- 
cated "in  like  manner"  of  the  Minor  term. 

Thus  far,  then,  the  Dictum  is  wholly  analytic  or  verbal, 
expressing  no  more  than  is  implied  in  the  definitions  ot 
'  Syllogism  '  and  '  Middle  Term ' ;  since  (as  we  have  seen) 
all  the  General  Canons  (except  the  third,  which  is  a  still 
more  general  condition  of  formal  proof)  are  derivable  from 
those  definitions.  However,  the  Dictum  makes  a  further 
statement  of  a  synthetic  or  real  character,  namely,  that  when 
these  conditions  are  fulfilled,  an  inference  is  justified ;  that  then 
the  Major  and  Minor  terms  are  brought  into  comparison  through 
the  Middle,  and  that  the  Major  may  be  predicated  affirma- 
tively or  negatively  of  all  or  part  of  the  Minor.  It  is  this  real 
assertion  that  justifies  us  in  calling  the  Dictum  an  Axiom. 

§  4.  Whether  the  Laws  of  Thought  may  not  fully  explain 
the  Syllogism  without  the  need  of  any  synthetic  principle,  has, 
however,  been  made  a  question.     Take  such  a  Syllogism  as 

the  following  : 

All  domesticated  animals  are  useful ; 
All  pugs  are  domesticated  animals  : 
.-.  All  pugs  are  useful. 
Here  (an  ingenious  man  might  urge),  having  once  identified 
pugs  with  domestic  animals,  that  they  are  useful  follows  from 
the   Law   of  Identity.     If  we   attend    to    the   meaning,   and 
remember  that  what  is  true  in  one  form  of  words  is  true  in  any 
other  form,   then,  all  domesticated  animals  being  useful,  of 
course  pugs  are.     It  is  merely  a  case  of  Subalternation  ;  we 
may  put  it  in  this  way : 

All  domesticated  animals  are  useful ; 
,\  Some  domesticated  animals  (e.g.,  pugs)  are  useful. 


CONDITIONS   OF   MEDIATE   INFERENCE       97 

The  derivation  of  Negative  Syllogisms  from  the  Law  of 
Contradiction  (we  might  add)  may  be  shown  in  a  similar 
manner. 

But  the  force  of  this  ingenious  argument  depends  on  the 
participial  clause—'  having  once  identified  pugs  with  domestic 
animals.'  If  this  is  a  distinct  step  of  the  reasoning,  the  above 
Syllogism  cannot  be  reduced  to  one  step,  cannot  be  exhibited 
as  mere  subalternation,  nor  be  brought  directly  under  the  law 
of  Identity.  If  '  pug ',  '  domestic  ',  and  '  useful '  are  distinct 
terms;  and  if  'pug'  and  'useful'  are  only  known  to  be 
connected  because  of  their  relations  to  '  domestic ' :  this  is 
something  more  than  the  Laws  of  Thought  provide  for :  it  is 
not  Immediate  Inference,  but  Mediate;  and  to  justify  it, 
scientific  method  requires  that  its  conditions  be  generalised. 
The  Dictum,  then,  as  we  have  seen,  does  generalise  these 
conditions,  and  declares  that  when  such  conditions  are  satisfied 
a  Mediate  Inference  is  valid. 

But,  after  all  (to  go  back  a  little),  consider  again  that 
proposition  All  pugs  are  domesticated  aftimals :  is  it  a  distinct 
step  of  the  reasoning ;  that  is  to  say,  is  it  a  Real  proposition  ? 
If  it  is ;  if  domesticated  '  is  no  part  of  the  definition  of  '  pug  ', 
the  proposition  is  Real,  and  is  a  distinct  part  of  the  argument. 
But  take  such  a  case  as  this : 

All  dogs  are  useful ; 

All  pugs  are  dogs. 
Here  we  clearly  have,  in  the  minor  premise,  only  a  verbal  pro- 
position :  to  be  a  dog  is  certainly  part  of  the  definition  of  '  pug '. 
But,  if  so,  the  inference  '  All  pugs  are  useful '  involves  no  real 
mediation,  and  the  argument  is  no  more  than  this : 
All  dogs  are  useful ; 
.'.  Some  dogs  {e.g.,  pugs)  are  useful. 
Similarly,  if  the  Major  Premise  be  Verbal,  thus  : 

All  men  are  rational ; 
Socrates  is  a  man — 
to   conclude  that   '  Socrates   is   rational '   is  no  Mediate   In- 
ference; for   so   much   was   implied   in   the  Minor  Premise. 

G 


98       LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


'  Socrates  is  a  man,'  and  the  Major  Premise  adds  nothing  to 
this. 

Hence  I  conclude  (as  by  anticipation  in  chap.  vii.  §  3)  that 
*any  apparent  syllogism,  having  one  premise  a  Verbal  Pro- 
position, is  really  an  Immediate  Inference ' ;  but  that,  if  both 
Premises  are  Real  Propositions,  the  Inference  is  Mediate,  and 
demands  for  its  explanation  something  more  than  the  Laws  of 
Thought.  I  have  not,  however,  always  refrained  from  using 
Verbal  Syllogisms  as  formal  illustrations. 

§  5.  Other  kinds  of  Mediate  Inference  exist,  yielding  valid 
conclusions,  without  being  truly  syllogistic.  Such  are  mathe- 
matical inferences  of  Equality,  as— 

A  =  B  =  C     .•.A  =  C. 
Here  there  are  strictly  four  terms— (i)  A,  (2)  equal  to  B,  (3)  B, 
(4)  equal  to  C. 

Similarly  with  the  argument  a  fortiori, 

A  >  B  >  C      .•.  (much  more)  A  >  C. 
This  also  contains  four  terms  :  (i)  A,  (2)  greater  than  B,  (3)  B, 
(4)  greater  than  C.    Such  inferences  are  nevertheless  intuitively 
sound,  may  be  verified  by  trial  (within  the  limits  of  sense- 
perception),    and  are   generalised    in   appropriate   axioms   of 
their  own,  corresponding  to  the  Dictum  of  the  Syllogism,  as 
'  Things  equal  to  the  same  thing  are  equal  to  one  another,'  etc. 
There  are  also  cases  of  Order  in  Time  and  Place  :  A  is  before 
B,  B  IS  before  C;  therefore,  A  is  before  C:  or,  again,  A  is  to  the 
left  ofB,  B  is  to  the  left  of  C ;  therefore  A  is  to  the  left  of  C. 
Some  cases,  however,  that  at  first  may  seem  equally  obvious, 
are  really  delusive,  unless  further  data  be  supplied.  For  instance, 
A  is  north  of  B,  B  is  west  of  C :  what  is  the  relation  of  A  to  C  ? 
One  may  be  tempted  to  answer,  '  North-east.'     But  suppose  A 
is  a  mi.e  to  the  north  of  B,  and  B  a  yard  to  the  west  of  C,  then 
A  is  practically  north  of  C;  at  least,   its   eastward   position 
uaniiot  be  expressed  in  terms  of  the  mariner's  compass.     In 
sucn  a  case,  then,  we  require  to  know  not  only  the  directions 
but  the  distances  of  A  and  C  from  B ;  and  then   the   exact 
direction  of  A  from  C  is  a  matter  of  mathematical  calculation. 


Ill 


CHAPTER  X 
CATEGORICAL  SYLLOGISMS 

§  I.  The  type  of  logical,  deductive,  mediate,  categorical 
Inference  is  a  Syllogism  directly  conformable  with  the  Dictum : 
as — 

All  carnivorous  animals  (M)  are  of  nervous  temperament  (P) ; 

Cats  (S)  are  carnivorous  animals  (M) : 
/.  Cats  (S)  are  of  nervous  temperament  (P). 
In  this  example  P  is  predicated  of  M,  a  term  distributed  •  in 
which  term,  M,  S  is  given  as  included  ;  so  that  P  may  be  pre^ 
dicated  of  S. 

Many  arguments,  however,  are  of  a  type  superficially  different 
from  the  above  :  as — 

No  wise  man  (P)  fears  death  (M); 
Dr.  Johnson  (S)  fears  death  (M) : 
.-.  Dr.  Johnson  (S)  is  not  a  wise  man  (P). 
In  this  example,  instead  of  P  being  predicated  of  M,  M  is  pre- 
dicated of  P,  and  yet  S  is  given  as  included  not  in  P,  but  in 
M.     The  divergence  of  such  a  Syllogism  from  the  Dictum 
may,  however,  be  easily  shown  to  be  superficial,  if  instead  of  No 
wise  man  fears  death  we  write  the  Simple  Converse,  JVo  man 
who  fears  death  is  wise. 

Again :  t^ 

Some  dogs  (M)  are  friendly  to  man  (P) ; 

All  dogs  (M)  are  carnivorous  (S) : 
.-.  Some  carnivores  (S)  are  friendly  to  man  (P). 
Here  P  is  predicated  of  M  undistributed ;  and  instead  of  S 
being  included  in  M,  M  is  included  in  S :   so  that  the  diver- 


loo      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

gence  from  the  type  of  Syllogism  to  which  the  Dictum  directly 
applies,  is  still  greater.  But  if  we  transpose  the  premises, 
taking  first 

All  dogs  (M)  are  carnivorous  (P), 
then  P  is  predicated  of  M  distributed ;  and,  simply  converting 
the  other  premise,  we  get — 

Some  things  friendly  to  man  (S)  are  dogs  (M) : 
whence  it  follows  that — 

Some  things  friendly  to  man  (S)  are  carnivores  (P) ; 
and  this  is  the  simple  converse  of  the  original  conclusion. 
Once  more : 

No  pigs  (P)  are  philosophers  (M) ; 

Some  philosophers  (M)  are   of   those    who    approve    of 
pleasure  (S) : 
.-.  Some  of  those  who  approve  of  pleasure  (S)  are  not  pigs  (P). 
In  this  case,  instead  of  P  being  predicated  of  M  distributed, 
M  is  predicated  of  P  distributed ;  and  instead  of  S  (or  part  of 
it)  being  included  in  M,  we  are  told  that  some  M  is  included 
in  S.     Still  there  is  no  real  difficulty.     To  show  that  it  is  all 
right,  simply  convert  both  the  premises.     Then  we  have : 
No  philosophers  (M)  are  pigs  (P) ; 
Some  who  approve  of  pleasure  (S)  are  philosophers  (M). 
Whence  the  same  conclusion  follows  ;  and  the  whole  Syllogism 
plainly  conforms  directly  to  the  Dictum. 

Such  departures  as  these  from  the  normal  syllogistic  form 
are  said  to  constitute  differences  of  Figure  (to  be  further  de- 
fined in  §  2) ;  and  the  processes  by  which  they  are  shown  to 
be  unessential  differences  are  called  Reduction  (for  a  fuller 
account  of  which,  see  §  6). 

§  2.  Figure  is  determined  by  the  position  of  the  Middle 
term  in  the  premises ;  of  which  position  there  are  four  possible 
variations.  The  Middle  Term  may  be  subject  of  the  Major 
Premise,  and  predicate  of  the  Minor,  as  in  the  first  example 
above;  and  this  position,  being  directly  conformable  to  the 
requirements  of  the  Dictum,  is  called  the  First  Figure.  Or  the 
Middle  Term  may  be  predicate  of  both  premises,  as  in  the 


CATEGORICAL   SYLLOGISMS 


lOl 


second  of  the  above  examples ;  and  this  is  called  the  Second 
Figure.  Or  the  Middle  may  be  subject  of  both  premises,  as  in 
the  third  of  the  above  examples ;  and  this  is  called  the  Third 
Figure.  Or,  finally,  the  Middle  may  be  predicate  of  the  Major 
premise,  and  subject  of  the  Minor,  as  in  the  fourth  example 
given  above ;  and  this  is  the  Fourth  Figure. 

It  may  facilitate  the  recollection  of  this  most  important  point 
if  we  schematise  the  Figures  thus  : 

in.  IV. 


I. 


II. 


M 


P 
M 


3 


M 
M 


rP 
S 


The  horizontal  lines  represent  the  premises,  and  at  the  angles 
formed  with  them  by  the  slanting  or  by  the  perpendicular  lines 
the  Middle  Term  occurs.  Note  further  that  the  schema  of 
the  Fourth  and  last  Figure  resembles  Z,  the  last  letter  of  the 
alphabet :  this  helps  one  to  remember  it  in  contrast  with  the 
First,  which  is  thereby  also  remembered. 

§  3.  The  Moods  of  each  Figure  are  the  modifications  of  it 
which  arise  from  different  combinations  of  propositions  accord- 
ing to  Quantity  and  Quality.  In  the  First  Figure,  for  example, 
four  Moods  are  recognised  :  A.  A.  A.,  E.  A.  E.,  A.  J.  I.,  E.  L  O. 

A.  AllM  isP; 

A.  All  S  is  M  : 

A.    .'.  All  Sis  P. 

^  E.  No  M  is  P ; 
/-     A.  Alls  is  M: 
E.    .-.  No  S  is  P. 


^V 


y 


V 


A.  All  M  is  P ; 
I.  Some  S  is  M  : 
I.    /.  Some  S  is  P. 


E.  No  M  is  P  ; 
I.  Some  S  is  M  : 
O.    .-.  Some  S  is  not  P. 
Now,  remembering  that  there  are  four  Figures,  and  four  kinds 


102      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

of  propositions  (A.  I.  E.  O.),  each  of  which  Propositions  may  be 
Major  Premise,  Minor  Premise,  or  Conclusion  of  a  Syllogism 
It  appears  that  in  each  Figure  there  may  be  64  Moods,  and 
therefore  256  in  all.  On  examinings  these  256  Moods,  how- 
ever, we  find  that  only  24  of  them  are  valid  (/>.,  of  such  a 
character  that  the  Conclusion  strictly  follows  from  the  Pre- 
mises) ;  whilst  5  of  these  24  are  needless,  because  their  Con- 
clusions are  'weaker'  or  less  extensive  than  the  Premises 
warrant ;  that  is  to  say,  they  are  particular  when  they  might  be 
universal.  Thus,  in  the  First  Figure,  besides  the  above  4 
Moods,  A.  A.  I.  and  E.  A.  O.  are  valid  in  the  sense  of  being 
conclusive;  but  they  are  superfluous,  because  included  in 
A.  A.  A.  and  E.  A.  E.  Omitting  then  these  5  needless  Moods, 
which  are  called  Subalterns  because  their  Conclusions  are 
subaltern  (chap.  vii.  §  2)  to  those  of  other  Moods,  there  remain 
19  Moods  that  are  valid  and  generally  recognised. 

§  4.  How  these  19  Moods  are  determined  must  be  our  next 
mquiry.  There  are  several  ways  more  or  less  ingenious  and 
interesting;  but  all  depend  on  the  application,  directly  or 
indirectly,  of  the  Six  Canons,  which  were  shown  in  the  last 
chapter  to  be  the  conditions  of  Mediate  Inference. 

(i)  One  way  is  to  begin  by  finding  what  Moods  of  the  First  Figure 
conform  to  the  Dictum.  Now.  the  Dictum  requires  that,  in  the  Major 
premise.  P  be  predicated  of  a  term  distributed,  from  which  it  follows 
that  no  Mood  can  be  valid  whose  Major  premise  is  Particular,  as  in 
I.  A.  I.,  or  O.  A.  O.  Again,  the  Dictum  requires  that  the  Minor  premise 
be  affirmative  ("  in  which  term  a  third  is  given  as  included  ") ;  so  that 
no  Mood  can  be  valid  whose  Minor  premise  is  negative,  as  in  A.'  E.  E.  or 
A.  O.  O.  By  these  considerations  we  find  that  in  the  First  Figure  out 
of  64  Moods  possible,  only  six  are  valid,  namely,  those  above  m^'entioned 
m  §  3.  including  the  two  Subalterns.  The  second  step  of  this  method 
is  to  test  the  Moods  of  the  Second,  Third  and  Fourth  Figures,  by  trying 
whether  they  can  be  reduced  to  one  or  other  of  the  four  Moods  of  the 
First  (as  briefly  illustrated  in  §  i.  and  to  be  further  explained  in  §  6) 

(2)  Another  way  is  to  take  the  above  six  General  or  Common  Canons 
and_to  deduce  from  them  Special  Canons  for  testing  each  Figure :  an 
interesting  method,  which,  on  account  of  its  length,  will  be  treated  of 
separately  in  the  next  section. 

(3)  Direct  application  of  the  Common  Canons  is.  perhaps,  the  sim- 


CATEGORICAL  SYLLOGISMS 


103 


plest  plan.  First  write  out  the  64  Moods  that  are  possible  without 
regard  to  Figure,  and  then  cross  out  those  which  violate  any  of  the 
Canons  or  Corollaries,  thus : 

AAA,  7^:iV«.  (6th  Can.  \).  AA  I.  T^%-e'(6th  Can.  h], 
-A-&A(6rtiCan.  a)  AE]^"^*«4.(6thCan.  fl)^EO. 
ft4=A.(Cor.  a.)  n^t&(6th  Can.  o}^  1 1.  :W^(6th  Can.  *) 
-tc^Jc{ti\h  C*a  a)  3~0*  (Cor.  u  ):ft-ai  (6th  Qua.  «)  A  O  O. 

The  student  will  find  it  a  useful  exercise  to  go  through  the  remaining 
48  Moods,  when  he  will  discover  that  of  the  whole  64  only  11  are  valid, 
namely  : 

A.  A.  A.,  A.  A.  I..  A.  E.  E..  A.  E.  O.,  A.  1. 1.,  A.  O.  O., 
E.  A.  E..  E.  A.  O.,  E.  I.  O.,  I.  A.  I.,  O.  A.  O. 

These  eleven  Moods  have  next  to  be  examined  in  each  Figure,  and  if 
valid  in  every  Figure  there  will  still  be  44  moods  in  all.  We  find,  how- 
ever, that  in  the  First  Figure,  A.vE.E.,  A.E.O.,  A.O.O.,  involve  illicit 
process  of  the  Major  Term  (3rd  Can.) ;  I.  A.  I.,  O.  A.  O.  involve  undistri- 
buted Middle  (4th  Can.) ;  and  A.  A.  I..  E.  A.  O.  are  Subalterns.  In  the 
Second  Figure  all  the  affirmative  Moods,  A.  A;  A.,  AM..!.,  A. 1. 1.,  LA.  I., 
involve  undistributed  Middle;  O.  A.  O.  involves  illicit  process  of  the 
Major;  and  A.  E.  O.,  E.  A.  O  are  Subalterns.  In  the  Third  Figure, 
A.  A.  A.,  E.A.  E.,  involve  illicit  process  of  the  Minor  (3rd  Can.); 
A.  E.  E..  A.  E.  O.,  A.  O.  O.  involve  illicit  process  of  the  Major.  In  the 
Fourth  Figure,  A.  A.  A.  involves  illicit  process  of  the  Minor;  A.  1. 1., 
A.  O.  O.  involve  Undistributed  Middle;  O.  A  O.  involves  illicit  process 
of  the  Major ;  and  A.  E.  O.  is  Subaltern. 

Those  moods  of  each  Figure  which,  when  tried  by  these 
tests,  are  not  rejected,  are  valid,  namely : 

Fig.  I.  — A.  A.  A.,     E.  A.  E.,    A.  L  L  , 
E.  A.  O.,  Subaltern); 

Fig.  IL— E.  A  ,E.,    A.  El.  E.,    E.  I.  O., 
A.  E.  O.,  Spbaltern) ;  ^^ 

Fig.  III.— A.  A.  L,    I.  A.  J.,     A.  LJ., 
E.  LO.; 

Fig.  T^L^=.>A.  A.  I.,    A.  E.-E.,     I.  A.  L, 

(A.  E.  O.,  Subaltern). 

Thus,  including  Subaltern  Moods,  there  are  six  valid  in  each 

Figure.      In    Fig.    III.    alone   there   is   no  Subaltern  Mood, 

because  in  that  Figure  there  can  be  no  universal  conclusion. 

§  5.  Special  Canons  of  the  several  Figures,  deduced  from  the  Com- 
mon Canons,  enable  us  to  arrive  at  the  same  result  by  a  somewhat 


\. 


E.  I.O.    (A,  A.  I., 

^^ 

A.  0,0.    (E,A.  O., 

E.A.  0.,    O.A.O., 

E.A.  O,     E.  I.O. 


I04      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

dififerent  course.     The  Special  Canons  are  not,  perhaps,  necessary  to 
the  Science,  but  they  afford  a  very  useful  means  of  enabling  a  student 
to  thoroughly  appreciate  the  character  of  formal  syllogistic  reasoning. 
Accordingly,  I  shall  indicate  the  proof  of  each  rule,  leaving  its  elabora- 
tion to  the  reader.    In  this  he  can  find  no  difficulty,  if  he  bears  in  mind 
that  Figure  is  determined  by  the  position  of  the  Middle  Term. 
Fig.  I.,  Rule  (a) :  The  minor  premise  must  he  affirmative. 
For,  if  not,  in  negative  Moods  there  will  be  illicit  process  of  the  Major 
Term.    Applying  this  rule  to  the  eleven  possible  Moods  given  in  §  4, 
as  remaining  after  application  of  the  Common  Canons,  it  eliminates 
A.  E.  E,  A.  E.O.,  A.  0.0. 

{h)  The  major  premise  must  he  universal. 

For,  if  not,  the  minor  being  affirmative,  the  Middle  Term  will  be 
undistributed.    This  rule  eliminates  I.  A.  I.,  O.  A.  O. ;  leaving  six  moods, 
including  two  Subalterns. 
Fig.  II.  {a)  One  premise  must  he  negative. 

For  else  neither  premise  will  distribute  the  Middle  Term.     This  rule 
eliminates  A.  A.  A.,  A.  A.  I.,  A.  1. 1.,  I.  A.  I. 
{h)  The  major  premise  7mist  he  universal. 

For  else,  the  conclusion  being  negative,  there  will  be  illicit  process  of 
the  Major  Term.  This  eHminates  I.  A.  I.,  O.  A.  O. ;  leaving  six  moods, 
including  two  Subalterns. 

Fig.  III.  {a)  The  minor  premise  must  he  affirmative. 

For  else,  in  negative  moods  there  will  be  illicit  process  of  the  Major 
Term.     This  rule  eHminates  A.  E.  E.,  A.  E.  O.,  A.  O.  O. 
{b)  The  conclusion  must  he  particular. 

For  else,  the  minor  premise  being  affirmative,  there  will  be  illicit 
process  of  the  Minor  Term.  This  eliminates  A.  A.  A.,  A.  E.  E.,  E.  A.  E. ; 
leaving  six  Moods. 

Fig.  IV.  {a)  When  the  major  premise  is  affirmative,  the  minor  must  he 
universal. 

For  else  the  Middle  Term  is  undistributed.     This  eliminates  All 
A.  0.0. 

{h)  When  the  minor  premise  is  affirmative,  the  conclusion  must  he  particular. 

For  else  there  will  be  illicit  process  of  the  Minor  Term.  This  elimi- 
nates A.  A.  A.,  E.  A.  E. 

(c)   When  either  premise  is  negative,  the  major  must  he  universal. 

For  else,  the  conclusion  being  negative,  there  will  be  illicit  process  of 
the  Major  Term.  This  eliminates  O.  A.  O.  ;  leaving  six  Moods,  including 
one  Subaltern. 


§  6.  Reduction  is  either— (i)  Ostensive  or  (2)  Indirect. 
Ostensive  Reduction  consists  in  showing  that  an  argument 
given  in  one  Mood  can  also  be  stated  in  another;  the  process 


I 


CATEGORICAL   SYLLOGISMS 


105 


\> 


f 


r 


L 


is  especially  used  to  show  that  the  moods  of  the  second,  third, 
and  fourth  Figures  are  equivalent  to  one  or  another  Mood  of 
the  first  Figure.  It  thus  proves  the  validity  of  the  former 
Moods  by  showing  that  they  also  essentially  conform  to  the 
Dictum,  and  that  all  Categorical  Syllogisms  are  only  superficial 
varieties  of  one  type  of  proof. 

To  facilitate  Reduction,  the  recognised  Moods  have  all  had 
names  given  them;    which  names,  again,  have  been  strung 
together  into  mnemonic  verses  of  great  force  and  pregnancy : 
Barbara,  Celarent,  Darii,  Ferioque  prioris : 
Cesare,  Camestres,  Festino,  Baroco,  secund^; 
Tertia,  Darapti,  -Disamis,  Datisi,  Felapton, 
Bocardo,  Ferison,  habet :  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

In  the  above  verses  the  names  of  the  Moods  of  Fig.  I.  begin  with  the 
first  four  consonants  B,  C,  D,  F,  in  alphabetical  order;  and  the  names 
of  all  other  Moods  likewise  begin  with  these  letters,  thus  signifying 
(except  in  Baroco  and  Bocardo)  the  Mood  of  Fig.  I.,  to  which  each  is 
equivalent,  and  to  which  it  is  to  be  reduced  :  as  Bramantip  to  Barbara, 
Camestres  to  Celarent,  and  so  forth. 

The  vowels  A,  E,  I,  O,  occurring  in  the  several  names,  give  the 
quantity  and  quality  of  Major  Premise.  Minor  Premise,  and  Conclusion 
in  the  usual  order. 

The  consonants  s  and  p,  occurring  after  a  vowel,  show  that  the  pro- 
position which  the  vowel  stands  for  is  to  be  converted  either  (s)  simply 
or  (p)  per  accidens ;  except  where  s  or  p  occurs  after  the  third  vowel  of  a 
name,  the  conclusion  :  then  it  refers  not  to  the  conclusion  of  the  given 
Mood  (say  Disamis),  but  to  the  conclusion  of  that  Mood  of  the  first 
Figure  to  which  the  given  Mood  is  reduced  (Darii). 

M  {mutare,  metathesis)  means  '  transpose  the  premises '  (as  of  Cames- 
tres). 

C  means  '  substitute  the  contradictory  of  the  conclusion  for  the  fore- 
going premise,'  a  process  of  the  Indirect  Reduction  to  be  presently 
explained  (see  Baroco,  p.  109). 

The  other  consonants  r,  n,  t,  (with  b  and  d,  when  not  initial)  occur- 
ring here  and  there,  have  no  mnemonic  significance. 

What  now  is  the  problem  of  Reduction  ?  The  difference  of  Figures 
depends  upon  the  position  of  the  Middle  Term.  To  reduce  a  Mood  of 
any  other  Figure  to  the  form  of  the  First,  then,  we  must  so  manipulate 
its  premises  that  the  Middle  Term  shall  be  subject  of  the  Major  pre- 
mise and  predicate  of  the  Minor.     Now  in  Fig.  II.  the  Middle  Term  is 


\ 


% 


io6      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

predicate  of  both  premises ;  so  that  the  Minor  may  need  no  alteration, 
and  to  convert  the  Major  may  suffice.  This  is  the  case  with  Cesare, 
which  reduces  to  Celarent  by  simply  converting  the  Major ;  and  with 
Festino,  which  by  the  same  process  becomes  Ferio.  In  Camestres, 
however,  the  Minor  premise  is  negative ;  and,  as  this  is  impossible  in 
Fig.  I.,  the  premises  must  be  transposed,  and  the  new  Major  premise 
must  be  simply  converted  :  then,  since  the  transposition  of  the  premises 
will  have  transposed  the  terms  of  the  conclusion  (according  to  the  usual 
reading  of  syllogisms),  the  new  conclusion  must  be  simply  converted  in 
order  to  prove  the  validity  of  the  original  Conclusion.  The  process 
may  be  thus  represented  (s.  c.  meaning  '  simply  convert ') : 


CATEGORICAL   SYLLOGISMS 


Camestres. 
All  P  is  M ; 

No  S  is  M  : 
No  S  is  P. 


f  fir 


Celarent. 
No  M  is  S  ; 

All  P  is  M : 
No  P  is  8. 


The  Ostensive  Reduction  of  Baroco  also  needs  special  explanation. 
As  it  used  to  be  reduced  indirectly,  its  name  gives  no  indication  of  the 
ostensive  process.  To  reduce  it  ostensively  let  us  call  it  Faksnoko, 
where  k  means  '  obvert  the  foregoing  premise. '  By  thus  obverting  (k) 
and  simply  converting  (s)  (in  sum,  contrapositing)  the  Major  Premise, 
and  obverting  the  Minor  Premise,  we  get  a  syllogism  in  Ferio,  thus  : 


Baroco  or  Faksnoko. 
All  P  is  M  ; 

Some  S  is  not  M  : 
.-.  Some  S  is  not  P. 


contrap.^ 


Ferio. 
->       No  m  (not-M)  is  P ; 


ah 


>fc'. 


->       Some S  is  m  (not-M) : 
.*.  Some  S  is  not  P. 


In  Fig.  III.  the  Middle  Term  is  subject  of  both  premises ;  so  that,  to 
reduce  its  Moods  to  the  First  Figure,  it  may  be  enough  to  convert  the 
Minor  premise.  This  is  the  case  with  Darapti,  Datisi,  Felapton  and 
Ferison.  But,  with  Disamis,  since  the  Major  premise  must  in  the 
First  Figure  be  universal,  we  must  transpose  the  premises,  and  then 
simply  convert  the  new  Minor ;  and,  lastly,  since  the  Major  and  Minor 
Terms  have  now  changed  places,  we  must  simply  convert  the  new  con- 
clusion in  order  to  verify  the  old  one.     Thus : 


f 


107 


Disamis. 
Some  M  is  P ; 

All  M  is  S : 
.'.  Some  S  is  P. 


s.c. 


Darii. 
All  M  is  S  ; 

Some  P  is  M 
•.  Some  P  is  S. 


Bocardo,  like  Baroco,  indicates  by  its  name  the  Indirect  process.    To 
reduce  it  ostensively  let  its  name  be  Doksamrosk,  and  proceed  thus : 


Bocardo  or  Doksamrosk. 
Some  M  is  not  P ; 

All  M  is  S  : 


So 


Darii. 

All  MisS; 

Somep(not-P)isM 


.-.  Some  S  is  not  P.        <     amveH  &  ohvert         .^  g^^^  ^  ^^^^^^  .^  ^ 

In  Fig.  IV.  the  position  of  the  Middle  Term  is,  in  both  premises,  the 
reverse  of  what  it  is  in  the  First  Figure  ;  we  may  therefore  reduce  its 
Moods  either  by  transposing  the  premises,  as  with  Bramantip,  Camenes, 
and  Dimaris  ;  or  by  converting  both  premises,  the  course  pursued  with 
Fesapo  and  Fresison.  It  may  suffice  to  illustrate  by  the  case  of 
Bramantip  : 


Bramantip. 
All  P  is  M  ; 

All  M  is  S : 


Some  Sis  P.   <   c^yert.p^a^. 


Barbara. 
All  M  is  S ; 

All  P  is  M  : 

•.  All  P  is  S. 


This  case  shows  that  a  final  significant  consonant  (s,  p,  or  sk)  in  the 
name  of  any  Mood  refers  to  the  conclusion  of  the  new  syllogism  in  the 
First  Figure ;  since  p  in  Bramantip  cannot  refer  to  its  own  Conclusion 
in  I.,  which,  being  already  particular,  cannot  be  converted /^r  accidens. 

Finally,  in  Fig.  I.,  Darii  and  Ferio  differ  respectively  from  Barbara 
and  Celarent  only  in  this,  that  their  Minor  Premises,  and  consequently 
their  conclusions,  are  subaltern  to  the  corresponding  propositions  of  the 
universal  Moods,  a  difference  which  seems  insufficient  to  give  them 


\ 


io8      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

rank  as  distinct  forms  of  demonstration.  And  as  for  Barbara  and  Cela- 
rent,  they  are  easily  reducible  to  one  another  by  obverting  their  Major 
premises  and  the  new  conclusion,  thus  : 


Barbara. 


All  MisP; 


obv. 


All  S  is  M  :     

All  S  is  P.      < 


obv. 


Celarent. 

No  M  is  p  (not  P) ; 
All  S  is  M  : 

No  S  is  p  (not  P). 


§  7.  A  new  version  of  the  mnemonic  lines  was  suggested  in  Mind 
No.  27,  with  the  object  of  (i)  freeing  them  from  all  meaningless  letters, 

(2)  showing  by  the  name  of  each  Mood  the  Figure  to  which  it  belongs, 

(3)  giving  names  to  indicate  the  ostensive  reduction  of  Baroco  and 
Bocardo.  To  obtain  the  first  two  objects,  /  is  used  as  the  mark  of 
Fig.  I.,  71  of  Fig.  II.,  r  of  Fig.  III.,  t  of  Fig.  IV.  The  verses  (to  be 
scanned  discreetly)  are  as  follows  : 

Balala,  Celalel,  Dalii,  Felioque  prioris : 

_  ^  ^    .  { Faksnoko  secundae : 

Cesane,  Camenes,  Fesmon,  -  ^ 

i  Banoco, 

Tertia,  Darapri,  Drisamis,  Darisi,  Ferapro, 

Doksamrosk  |      perisor  habet :  Quarta  insuper  addit 

Eocaro  J 

Bamatip,  Gametes,  Dimatis,  Fesapto,  Fesistot. 

De  Morgan  praised  the  old  verses  as  "  more  full  of  meaning  than  any 
others  that  ever  were  made  "  ;  and  in  defence  of  the  above  alteration  it 
may  be  said  that  they  now  deserve  that  praise  still  more. 

§  8.  Indirect  Reduction  is  the  process  of  proving  a  Mood  to 
be  valid  by  showing  that  the  supposition  of  its  invalidity  involves 
a  contradiction.  Take  Baroco,  and  (since  the  doubt  as  to  its 
validity  is  not  concerned  with  the  truth  of  the  premises,  but 
with  their  relation  to  the  conclusion)  assume  the  premises  to 
be  true.  Then,  if  the  conclusion  be  false,  its  contradictory  is 
true.  The  conclusion  being  in  O.,  its  contradictory  will  be  in 
A.  Substituting  this  A.  for  the  Minor  premise  of  Baroco,  we 
have  the  premises  of  a  syllogism  in  Barbara,  which  will  be 
found  to  give  a  conclusion  in  A.,  contradictory  of  the  original 
Minor  premise  ;  thus  : 


1 


i 

1 


-i 


\ 


CATEGORICAL   SYLLOGISMS 


109 


Baroco. 
All  P  is  M  ; 

Some  S  is  not  M  : 

Some  S  is  not  P. 


Barbara. 
All  P  is  M  ; 

All  S  is  P : 

All  S  is  M. 


\ 


But  the  original  Minor,  Some  S  is  nol  M^  is  true  by  hypothesis ; 
and  therefore  the  conclusion  of  Barbara,  All  S  is  M^  is  false. 
This  falsity  cannot,  however,  be  due  to  the  form  of  Barbara, 
which  wc  know  to  be  valid ;  nor  to  the  Major  premise,  which 
is  taken  from  Baroco,  and  is  true  by  hypothesis  :  it  must, 
therefore,  be  in  the  Minor  premise  of  Barbara,  All  S  is  P ; 
and  since  this  is  contradictory  of  the  conclusion  of  Baroco 
Some  S  is  not  P^  that  conclusion  was  true. 

Similarly  with  Bocardo,  the  Indirect  Reduction  proceeds  by  substi- 
tuting for  the  Major  Premise  the  contradictory  of  the  Conclusion  ;  thus 
again  obtaining  the  premises  of  a  syllogism  in  Barbara,  whose  con- 
clusion is  contradictory  of  the  original  Major  premise.  Hence  the 
initial  B  in  Baroco  and  Bocardo :  it  points  to  a  syllogism  in  Barbara 
as  the  means  of  Indirect  Reduction  {Reductio  ad  impossibile). 

Any  other  Mood  may  be  reduced  indirectly  :  as,  for  example,  Dimaris. 
If  this  is  supposed  to  be  invalid  and  the  conclusion  false,  substitute  the 
contradictory  of  the  conclusion  for  the  Major  premise,  thus  obtaining 
the  premises  of  Celarent : 


Dimaris. 
Some  P  is  M  ;   ts 

All  M  is  S  : 


Some  S  is  P. 


Celarent. 
No  S  is  P ; 

All  M  is  S  : 
No   M  is  P 


No  P  is  M  <- 


The  conclusion  of  Celarent,  simply  converted,  contradicts  the  original 
Major  premise  of  Dimaris,  and  is  therefore  false.  Therefore  the  Major 
of  Celarent  is  false,  and  the  conclusion  of  Dimaris  is  true.     We  might 


no      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

^he  MnS  '°?f ""'  "'"7°"ic  names  for  the  Indirect  Reduction  of  all 
the  Moods :  the  name  of  Dimaris  would  then  be  Cicari. 

§  9.  The  need  or  use  of  any  Figure  but  the  First,  has  been 
much  discussed  by  Logicians.  Since,  in  actual  debate,  argu- 
ments are  rarely  stated  in  syllogistic  form ;  and,  therefore!  if 
reduced  to  that  form  for  closer  scrutiny,  generally  have  to  be 
treated  with  some  freedom ;  why  not  always  throw  them  at 
once  into  the  First  Figure  ?  That  Figure  has  manifest  advan- 
tages:  it  agrees  directly  with  the  Dictum;  it  gives  conclusions 
m  all  four  prepositional  forms,  and  therefore  serves  every  pur- 
pose of  full  affirmation  or  denial,  of  showing  agreement  or 
difference  (total  or  partial),  of  establishing  the  contradictories 
of  universal  statements ;  and  it  is  the  only  Figure  in  which  the 
subject  and  predicate  of  the  conclusion  occupy  the  same 
positions  in  the  premises,  so  that  the  course  of  argument  has 
in  Its  mere  expression  an  easy  and  natural  flow 

Still,  the  Second  Figure  has  also  a  very  natural  air  ,n  some 
kinds  of  negative  arguments.  The  parallelism  of  the  two 
premises  with  the  same  predicate  for  Middle  term,  brings  out 
very  forcibly  the  necessary  difference  between  the  Major  and 
Mmor  terms  that  is  involved  in  their  opposite  relations  to  the 
Middle.  P  ts  not,  whilst  S  is,  M,  says  Cesare :  that  very 
neatly  drives  home  the  conviction  that  S  is  not  P.  Or  perhaps 
even  more  naturally  in  Camestres :  Deer  do,  oxen  do  not,  shed 
their  horns.     What  is  the  conclusion .' 

The  Third  Figure,  again,  furnishes  in  Darapti  and  Felapton 
the  most  natural  forms  of  stating  arguments  in   which  the 
Middle  term  is  singular : 

Socrates  was  truthful; 

Socrates  was  a  Greek  : 
.'.  Some  Greek  was  truthful. 
Reduchg  this  to  Fig.  I.,  we  should  get  for  the  Minor  premise. 
Some  Greek  was  Socrates  :  which  is  certainly  inelegant.     Still,  it 
might  be  urged  that  in  the  science  of  proof,  elegance  is  an  alto- 
gether extraneous  consideration.   And  as  for  the  other  advantage 


CATEGORICAL  SYLLOGISMS 


III 


{ 

! 


I 


claimed  for  Fig.  III.— that,  as  ityields  only  particular  conclusions, 
it  is  useful  in  establishing  contradictories  against  universals— I  do 
not  see  that  for  that  purpose  any  of  its  Moods  have  a  superiority 
over  Darii  and  Ferio. 

As  for  Fig.  IV.,  no  particular  advantage  is  claimed  for  it.  It 
is  of  comparatively  late  recognition  (sometimes  called  the 
*Galenian',  after  Galen,  its  supposed  discoverer);  and  its 
scientific  claim  to  exist  at  all  is  disputed.  It  is  said  to  be  a 
mere  inversion  of  Fig.  I. ;  which  is  not  true  in  any  sense  in 
which  Figs.  II.  and  III.  may  not  be  condemned  as  partial 
inversions  of  Fig.  I.,  and  as  having  therefore  still  less  claim  to 
recognition.  It  is  also  said  to  invert  the  order  of  thought ;  as 
if  thought  had  only  one  order,  or  as  if  the  mere  order  of 
thought  had  anything  to  do  with  Formal  Logic.  The  truth 
is  that,  if  distinction  of  Figure  be  recognised  at  all,  the 
Fourth  Figure  is  scientifically  necessary,  because  it  is  inevitably 
generated  by  an  analysis  of  the  possible  positions  of  the  Middle 

Term. 

§  10.  Is  Reduction  necessary,  however;  or  have  not  all  the 
Figures  equal  and  independent  validity?     In  one  sense  not 
only  every  Figure  but  each  Mood  has  independent  validity : 
for  any  one  capable  of  abstract  thinking  sees  its  validity  by 
direct  inspection.     But  this  is  true  not  only  of  the  abstract 
Moods,  but  very  commonly  of  particular  concrete  arguments. 
Science,    however,   aims   at   unifying    knowledge;    and    after 
reducing    all     possible     arguments     that     form     categorical 
syllogisms  to  the  nineteen  Moods,  it  is  but  another  step  in 
the  same  direction  to  reduce  these  Moods  to  one  form.     This 
is  the  very  nature  of  science :  and,  accordingly,  I  cannot  look 
without  wonder  at  the  efforts  of  some  Logicians  to  expound 
separate  principles  of  each  Figure.      Grant  that  they  succeed ; 
and  what  can  the  next  step  be,  but  either  to  reduce  these 
principles  to  the  Dictum,  or  the  Dictum  and  the  rest  to  one  of 
these  principles  ?     Unless  this  can  be  done  there  is  no  science 
of  Formal  Logic.     If  it  is  done,  what  is  gained  by  reducing 
the  principles  of  the  other  Figures  to  the  Dictum,  instead  of 


112      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


CATEGORICAL  SYLLOGISMS 


"3 


the  Moods  of  the  other  Figures  to  those  of  the  first  Figure  ? 
It  may,  perhaps,  be  said  that  to  show  (i)  that  the  Moods  of 
the  second,  third,  and  fourth  Figures  flow  from  their  own 
principles  (though,  in  fact,  these  principles  are  laboriously 
adapted  to  the  Moods) ;  and  (2)  that  these  principles  may  be 
derived  from  the  Dictum^  is  the  more  uncompromisingly  regular 
method ;  but,  on  the  whole,  is  not  Formal  Logic  aheady 
sufficiently  encumbered  with  formalities  ? 

§  II.  Euler's  diagrams  may  be  used  to  illustrate  the  syllogism,  thus : 


Fig.  8. 


Fig.  5. 


Barbara — 


Fig.  6. 


Celarent 


Fig.  7. 


Remembering  that  '  Some'  means  *  It  may  be  all,'  it  is  plain  that  any 
one  of  these  diagrams  in  Fig.  7,  or  the  one  given  above  for  Barbara,  may 
represent  the  denotative  relations  of  P,  M  and  S  in  Darii;  though  no  doubt 
the  diagram  we  generally  think  of  as  representing  it  is  No.  i.  in  Fig.  7. 


Ferio 


Here  again,  I  suppose,  we  generally  think  of  No.  i  as  the  diagram 
representing  Ferio ;  but  2,  or  3,  or  that  given  above  for  Celarent,  is 
compatible  with  the  premises. 

Students  will  do  well  to  work  out  the  diagrams  for  the  Moods  of  the 
other  Figures,  noticing  how  they  stand  related  to  the  above. 


II 


CHAPTER  XI 
ABBREVIATED   AND   COMPOUND   ARGUMENTS 

§  I    In  ordinary  discussion,  whether  oral  or  written,  it  is 
but  rarely  that  the  forms  of  Logic  are  closely  adhered  to.     We 
often  leave  wide  gaps  in  the  structure  of  our  arguments,  trust- 
ing the  intelligence  of  those  addressed  to  bridge  them  over  ; 
or  we  invert  the  regular  order  of  propositions,  begmnmg  with 
the  conclusion,  and  mentioning  the  premises,  perhaps,  a  good 
while  after,  confident  that  the  sagacity  of  our  audience  will 
make  all  smooth.      Sometimes  a  full  style,  like  Macaulay's, 
may    by  means  of  amplification  and  illustration,  spread  the 
elements  of  a  single  syllogism  over  several  pages-a  penny- 
worth of  logic  steeped  in  so  much  eloquence.     These  practices 
give  a  great  advantage  to  sophists ;  who  would  find  it  very 
inconvenient  to  state  explicitly  in  Mood  and  Figure  the  preten- 
tious antilogies  which  they  foist  upon  the  public ;  and,  indeed, 
such  licences  of  composition  often  prevent  honest  men  from 
detecting  errors  into  which  they  themselves  have  unwittingly 
fallen,  and  which,  with  the  best  intentions,  they  strive  to  com- 
municate to  others  :  but  we  put  up  with  these  drawbacks  to 
avoid  the  inelegance  (forsooth)  and  the  tedium  of  a  long  dis- 
course in  accurate  syllogisms. 

Many  departures  from  the  strictly  logical  statement  of 
reasonings,  consist  in  the  use  of  vague  or  figurative  language, 
or  in  the  substitution  for  one  another  of  expressions  supposed 
to  be  equivalent  though,  in  fact,  dangerously  discrepant. 
Against  such  occasions  of  error  the  logician  can  provide  no 
safeguard,  except  the  advice  to  be  careful  and  discriminating 


ABBREVIATED  ARGUMENTS 


"5 


in  what  you  say  or  hear.     But  as  to  any  derangement  of  the 
elements   of  an   argument,  or  the  omission  of  them,  Logic 
effectually  aids  the  task  of  restoration  ;   for  it  has  shown  what 
the  elements  are  that  enter  into  the  explicit  statement  of  most 
ratiocinations,  namely,  the  four  forms  of  propositions  ;  and 
what  that  connected  order  of  propositions  is  which  most  easily 
and  surely   exposes   the   validity   or   invalidity   of  reasoning, 
namely,  the  Premises  and  Conclusion  of  the  Syllogism.    Logic 
has  even  gone  so  far  as  to  name  certain  abbreviated  forms  of 
proof,  which  may  be  regarded  as  general  types  of  those  that 
actually  occur  in  debate,  in  leading  articles,  pamphlets  and 
other  persuasive  or   polemical  writings— namely,  the  Enthy- 
meme,  Epicheirema  and  Sorites. 

§  2.  The  Enthymeme,  according  to  Aristotle,  is  the  Syllo- 
gism of  probable  reasoning  about  practical  affairs  and  matters 
of  opinion,  in  contrast  with  the  Syllogism  of  theoretical  de- 
monstration from  necessary  grounds.  But,  as  now  commonly 
treated,  it  is  an  argument  with  one  of  its  elements  omitted ; 
a  Categorical  Syllogism,  having  one  or  other  of  its  Premises,  or 
else  its  Conclusion,  suppressed.  If  the  Major  Premise  is  sup- 
pressed, it  is  called  an  Enthymeme  of  the  First  Order ;  if  the 
Minor  Premise  is  wanting,  it  is  said  to  be  of  the  Second  Order; 
if  the  Conclusion  is  left  to  be  understood,  there  is  an  Enthy- 
meme of  the  Third  Order. 

Let  the  following  be  a  complete  Syllogism  : 
All  free  nations  are  enterprising ; 
The  Dutch  are  a  free  nation  : 
.-.  The  Dutch  are  enterprising. 
Reduced  to  Enthymemes  this  argument  may  be  put  thus : 

In  the  First  Order— 

The  Dutch  are  a  free  nation  : 
/.  The  Dutch  are  enterprising. 

In  the  Second  Order — 

All  free  nations  are  enterprising  : 
.-,  The  Dutch  are  enterprising. 


ii6      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

In  the  Third  Order- 
All  free  nations  are  enterprising ; 
And  the  Dutch  are  a  free  nation. 

It  is  certainly  very  common  to  meet  with  arguments  whose  statement 
may  be  represented  by  one  or  other  of  these  three  forms ;  indeed  the 
Enthymene  is  the  natural  substitute  for  a  full  Syllogism  in  oratory : 
whence  the  transition  from  Aristotle's  to  the  modern  meaning  of  the 
term.  The  most  unschooled  of  men  readily  apprehend  its  force ;  and  a 
student  of  Logic  can  easily  supply  the  proposition  that  may  be  wanted, 
in  any  case,  to  complete  a  Syllogism,  and  thereby  test  the  argument's 
formal  validity.  In  an  Enthymene  of  the  Third  Order,  especially,  to 
supply  the  Conclusion  cannot  present  any  difficulty  at  all ;  and  hence 
it  is  a  favourite  vehicle  of  innuendo ;  as  in  Hamilton's  example  — 

Every  liar  is  a  coward  ; 
And  Caius  is  a  liar. 
The  frankness  of  this  statement  and  its  reticence,  together,  make  it  a 
biting  sarcasm  upon  Caius. 

To  find  the  missing  Premise  in  an  Enthymene  of  either  the  First  or 
Second  Order,  a  simple  rule  may  be  given  :  Take  that  Term  of  the 
given  Premise  that  does  not  occur  in  the  Conclusion  (and  which  must 
therefore  be  the  Middle),  and  combine  it  with  that  Term  of  the  Conclu- 
sion that  does  not  occur  in  the  given  Premise;  the  proposition  thus 
formed  is  the  Premise  which  was  requisite  to  complete  the  Syllogism. 
If  the  Premise  thus  constituted  contain  the  predicate  of  the  Conclusion, 
the  Enthymene  was  of  the  First  Order ;  if  it  contain  the  Subject  of  the 
Conclusion,  the  Enthymene  was  of  the  Second  Order. 

To  reduce  the  argument  of  any  ordinary  discourse  to  logical  forms, 
the  first  care  should  be  to  make  it  clear  to  oneself  what  exactly  the 
Conclusion  is,  and  to  state  it  adequately  but  as  succinctly  as  possible. 
Then  look  for  the  evidence.  This  may  be  of  an  inductive  character, 
consisting  of  instances,  examples,  analogies ;  and,  if  so,  of  course  its 
cogency  must  be  evalued  by  the  principles  of  Induction,  which  we  shall 
presently  investigate.  But  if  the  evidence  is  deductive,  it  will  probably 
consist  of  an  Enthymene,  or  of  several  Enthymenes  one  depending  on 
another.  Each  Enthymene  may  be  isolated  and  expanded  into  a 
Syllogism.  And  we  may  then  inquire;  (i)  whether  the  Syllogisms  are 
formally  correct  according  to  Barbara  (or  whatever  the  appropriate 
Mood) ;  (2)  whether  the  Premises,  or  the  ultimate  Premises,  are  true  in 
fact. 

§  3.  A  Monosyllogism  is  a  syllogism  considered  as  standing 
alone  or  without  relation  to  other  arguments.     But,  of  course, 


ABBREVIATED   ARGUMENTS 


117 


a  disputant  may  be  asked  to  prove  the  premises  of  any  syllo- 
gism ;  in  which  case  other  syllogisms  may  be  advanced  for 
that  purpose.  When  the  conclusion  of  one  syllogism  is  used 
to  prove  another,  we  have  a  chain-argument ;  which,  stated  at 
full  length,  is  a  Polysyllogism.  In  any  Polysyllogism,  again, 
a  syllogism  whose  conclusion  is  used  as  the  premise  of  another, 
is  called  in  relation  to  that  other  a  Prosyllogism ;  whilst  a  syllo- 
gism, one  of  whose  premises  is  the  conclusion  of  another 
syllogism,  is  in  relation  to  that  other  an  Episyllogism.  Two 
modes  of  abbreviating  a  Polysyllogism  are  usually  discussed, 
the  Epicheirema  and  the  Sorites. 

§  4.  An  Epicheirema  is  a  syllogism  for  one  or  both  of  whose 
premises  a  reason  is  added ;  as — 

All  men  are  mortal,  for  they  are  animals ; 
Socrates  is  a  man,  for  rational  bipeds  are  men  ; 
.'.  Socrates  is  mortal. 

The  Epicheirema  is  called  Single  or  Double,  says  Hamilton, 
according  as  an  "  adscititious  proposition  "  attaches  to  one  or 
both  of  the  premises.  The  above  example  is  of  the  double 
kind.  The  Single  are  said  to  be  of  the  First  Order,  if  the 
adscititious  proposition  attaches  to  the  Major  Premise ;  if  to  the 
Minor,  of  the  Second  Order.    (Hamilton  :  Lecture  xix.) 

An  Epicheirema  then  is  an  abbreviated  chain  of  reasoning, 
or  Polysyllogism,  comprising  an  Episyllogism  with  one  or  two 
enthymematic  Prosyllogisms.  The  Major  Premise  in  the 
above  case.  All  meti  are  mortal,  for  they  are  animals,  is  an 
Enthymeme  of  the  First  Order,  suppressing  its  own  Major  Pre- 
mise, and  may  be  restored  thus  : 

All  animals  are  mortal  \ 
All  men  are  animals  ; 
.*.  All  men  are  mortal. 

The  Minor  Premise,  however,  is  an  Enthymeme  of  the  Second 
Order,  suppressing  its  Minor  Premise,  and  may  be  restored 
thus  : 


! 


ii8      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

All  rational  bipeds  are  men  ; 
Socrates  is  a  rational  biped : 
;.  Socrates  is  a  man. 
§  5.  The  Sorites  is  a  Pol> syllogism  in  which  the  Conclusions 
and  even  some  of  the  Premises,  are  suppressed  until  the  argu- 
ment  ends.      If  the   chain  of  arguments  were   freed   of  its 
enthymematic  character,  the  suppressed  Conclusions  would  of 
course  appear  as  Premises  of  Episyllogisms. 

Two  varieties  of  Sorites  are  recognised,  the  Aristotelian  (so 
called,  though  not  treated  of  by  Aristotle),  and  the  Goclenian 
(named  after  its  discoverer,  Goclenius  of  Marburg,  who  flourished 
about  1600  A.D.).  In  order  to  compare  these  two  forms  of 
argument,  it  will  be  convenient  to  place  side  by  side  Hamilton's 
classical  examples  of  them. 


Aristotelian. 
Bucephalus  is  a  horse ; 
A  horse  is  a  quadruped ; 
A  quadruped  is  an  animal ; 
An  animal  is  a  substance ; 
Bucephalus  is  a  substance. 


Goclenian. 
An  animal  is  a  substance ; 
A  quadruped  is  an  animal ; 
A  horse  is  a  quadruped  ; 
Bucephalus  is  a  horse ; 
Bucephalus  is  a  substance. 


The  reader  wonders  what  is  the  diff'erence  between  these  two 
forms.     Of  course,  in  the  Aristotelian  Sorites  the  Minor  Term 
occurs  in  the  first  Premise,  and  the  Major  Term  in  the  last ; 
whilst  in  the  Goclenian  the  Major  Term  occurs  in  the  first,  and 
the  Minor  in  the  last.     But  since  the  character  of  Premises  is 
fixed   by  their   Terms,  not  by  the  order  in  which  they  are 
written,  there  cannot  be  a  better  example  of  a  distinction  with- 
out a  difference.     At  a  first  glance,  indeed,  there  may  seem  to 
be   a  more  important   point   involved:  the  Premises   of  the 
Aristotelian  Sorites  seem  to  proceed  in  the  order  of  the  Fourth 
Figure.     But  if  that  were  really  so  the  Conclusion  would  be, 
Some  substance  is  Bucephalus.    That,  on  the  contrary,  every  one 
writes  the  Conclusion,  Bucephalus  is  a  substance,  proves  that 
the  logical  order  of  the  Premises  is  in  the  First  Figure.     Logi- 
cally, therefore,  there  is  absolutely  no  difference  between  these 


ABBREVIATED   ARGUMENTS 


119 


two  forms,  and  pure  reason  requires  that  the  "Aristotelian 
Sorites"  disappear  from  the  text-books.  It  is  the  shining 
merit  of  Goclenius  to  have  restored  the  Premises  of  the  Sorites 
to  the  usual  order  of  Fig.  i . :  whereby  he  has  raised  to  himsel 
a  monument  more  durable  than  brass,  and  secured  indeed  the 
very  cheapest  immortality.  How  expensive,  compared  with 
this,  was  the  method  of  that  Ephesian  incendiary ! 

The  common  Sorites,  then,  being  in  the  First  Figure,  its  rules  follow 
from  those  of  the  First  Figure  : 

(i)  Only  one  Premise  can  be  particular;  and,  if  any,  only  that  in 
which  the  Minor  Term  occurs. 

For,  just  as  in  Fig.  I.,  a  particular  Premise  anywhere  else  involves 
Undistributed  Middle. 

(2)  Only  one  Premise  can  be  negative;  and,  if  any,  only  that  in 
which  the  Major  Term  occurs. 

For  if  there  were  two  negative  premises,  at  the  point  where  the 
second  entered  the  chain  of  argument  there  must  be  a  Syllogism  with 
two  negative  premises,  which  is  contrary  to  Rule  5  ;  whilst  if  one  pre- 
mise be  negative  it  must  be  that  which  contains  the  Major  Term,  for 
the  same  reason  as  in  Fig.  I. ,  namely,  that  the  Conclusion  will  be  nega- 
tive, and  that  therefore  only  a  negative  Major  Premise  can  prevent 
Illicit  Process  of  the  Major  Term. 

If  we  expand  a  Sorites  into  its  constituent  Syllogisms,  the  conclusions 
successively  suppressed  will  reappear  as  Major  Premises  ;  thus  : 

(i)  An  animal  is  a  substance ; 

A  quadruped  is  an  animal ; 
/.   A  quadruped  is  a  substance. 
{2)  A  quadruped  is  a  substance ; 

A  horse  is  a  quadruped  ; 
.'.   A  horse  is  a  substance. 
(3)  A  horse  is  a  substance  ; 

Bucephalus  is  a  horse  ; 
.'.   Bucephalus  is  a  substance. 

This  suffices  to  show  that  the  Protosyllogism  of  a  Goclenian  Sorites 
is  an  Enthymeme  of  the  Third  Order ;  after  which  the  argument  is  a 
chain  of  Enthymemes  of  the  First  Order,  or  even  of  the  First  and  Third 
combined,  since  the  Conclusions  as  well  as  the  Major  Premises  are 
omitted,  except  in  the  last  one. 

Lest  it  should  be  thought  that  the  Sorites  is  only  good  for  arguments 
so  frivolous  as  the  above,  I  subjoin  an  example  collected  from  various 
parts  of  Mill's  Political  Economy  : — 


I20 


LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


The  cost  of  labour  depends  on  the  efficiency  of  labour ; 

The  rate  of  profits  depends  on  the  cost  of  labour  ; 

The  investment  of  capital  depends  on  the  rate  of  profits  ; 

Wages  depend  on  the  investment  of  capital ; 
.-.   Wages  depend  on  the  efficiency  of  labour. 
Had  it  occurred  to  Mill  to  construct  this  Sorites,  he  would  have  modified 
his  doctrine  of  the  Wages-Fund,  and  would  have  saved  many  critics 
from  the  malignant  joy  of  refuting  him. 

§  6.  The  Antinomy  is  a  combination  of  arguments  by  which 
contradictory  attributes  are  provtd  to  be  predicable  of  the  same 
subject.     In  symbols,  thus  : 

All  U  is  P  AH  N  is  p 

All  S  is  M  All  S  is  N 

All  S  is  P  All  S  is  p 

Now,  by  the  principle  of  Contradiction,  S  cannot  be  P  and  p 
(not-P)  :  therefore,  if  both  of  the  above  syllogisms  are  sound, 
S  cannot  exist  at  all.  The  contradictory  conclusions  are  called, 
respectively,  Thesis  and  Antithesis. 

To  come  to  particulars,  w^e  may  argue  ;  (i)  that  a  constitu- 
tion which  is  at  once  a  monarchy,  an  aristocracy  and  a  de- 
mocracy, must  comprise  the  best  elements  of  all  three  forms ; 
and  must,  therefore,  be  the  best  of  all  forms  of  government ; 
the  British   Constitution  is,  therefore,  the   best  of  all.      But 
(2)  such  a  constitution  must  also  comprise  the  worst  elements 
of  monarchy,  aristocracy  and  democracy  ;  and,  therefore,  must 
be  the  worst  of  all  forms.     Are  we,  then,  driven  to  conclude 
that  the  British  Constitution,  thus  proved  to  be  both  the  best 
and  worst,  does  not  really  exist  at  all,  being  logically  impos- 
sible ?     For  the  proofs  seem  to  me  equally  good. 
Again, 

(i)  Every  being  who  is  responsible  for  his  actions  is  free ; 
Man  is  responsible  for  his  actions  : 
.-.  Man  is  free. 
(2)  Every  being  whose  actions  enter  into  the  course  of  nature 

is  not  free ; 
Man  is  such  a  being  : 
.-.  Man  is  not  free. 


ABBREVIATED   ARGUMENTS 


121 


Does  it,  then,  follow  that  '  Man,'  as  the  subject  of  contradictory 
attributes,  is  a  nonentity  ?  This  doctrine,  or  something  like 
it,  has  been  seriously  entertained  ;  but  if  to  any  reader  it  seems 
extravagant  (as  it  certainly  does  to  me),  lie  will  no  doubt  find 
an  error  in  the  above  arguments. 

For  other  examples  it  is  enough  to  refer  to  the  Critique  of 
Pure  Reasoft,  where  Kant  sets  out  the  Antinomies  of  Rational 
Cosmology.  But  even  if  we  do  not  agree  with  Kant  that  the 
human  understanding,  in  attempting  to  deal  with  certain 
subjects  beyond  its  reach,  inevitably  falls  into  such  contradic- 
tory reasonings;  yet  it  can  hardly  be  doubted  that  we  not 
unfrequently  hold  opinions  which,  if  logically  developed,  result 
in  Antinomies.  And,  accordingly,  the  Antinomy,  if  it  cannot 
be  imputed  to  Reason  herself,  may  be  a  very  fair,  and  a  very 
wholesome,  argumentum  ad  hominetn. 


J 


CHAPTER  XII 
CONDITIONAL  SYLLOGISMS 

§  I.  Conditional  Syllogisms  may  be  generally  described  as 
those  that  contain  conditional  propositions.  They  are  usually 
divided  into  two  classes,  Hypothetical  and  Disjunctive. 

A  Hypothetical  Syllogism  is  one  that  consists  of  a  Hypo- 
thetical Major  Premise,  a  Categorical  Minor  Premise,  and  a 
Categorical  Conclusion.     Two  Moods  are  usually  recognised  : 
(i)  Modus  J>onef IS,  or  Constructive. 

If  A  is  B,  C  is  D ; 
AisB: 
.-.  C  is  D. 

If  Aristotle's  reasoning  is  conclusive,  Plato's  theory  of  Ideas 
is  erroneous ; 
Aristotle's  reasoning  is  conclusive : 
.'.  Plato's  theory  of  Ideas  is  erroneous. 

Rule  of  the  Modus  ponens :  The  Antecedent  of  the  Major 
Premise  being  affirmed  in  the  Minor  Premise,  the  Consequent 
is  also  affirmed  in  the  Conclusion. 
(2)  Modus  tollens,  or  Destructive. 

If  A  is  B,  Cis  D; 
C  is  not  D ; 
.".  A  is  not  B. 

If  Pythagoras  is  to  be  trusted,  Justice  is  a  number; 
Justice  is  not  a  number: 
.*,  Pythagoras  is  not  to  be  trusted. 
Rule  of  the  Modus  tollens :  The  Consequent  of  the  Major 


CONDITIONAL  SYLLOGISMS 


123 


f 


Premise  being  denied  in  the  Minor  Premise,  the  Antecedent 
is  denied  in  the  Conclusion. 

By  using  negative  Major  Premises  two  other  forms  are 
obtainable:  then,  either  by  affirming  the  Antecedent  or  by 
denying  the  Consequent,  we  draw  a  negative  Conclusion. 

Thus  {Modus  ponens) :  {Modus  tollens) : 

If  A  is  B,  C  is  not  D;  If  A  is  B,  C  is  not  D; 

AisB:  CisD: 

.'.  C  is  not  D.  .-.  A  is  not  B. 

Further,  since  the  Antecedent  of  the  Major  Premise,  taken  by  itself, 
may  be  negative,  it  seems  possible  to  obtain  four  more  forms,  two 
in  each  Mood,  from  the  following  Major  Premises : 

(i)  If  A  is  not  B,  Cis  D; 
(2)  If  A  is  not  B,  C  is  not  D. 

But  since  the  quality  of  a  Hypothetical  Proposition  is  determined  by 
the  quality  of  its  Consequent,  not  at  all  by  the  quality  of  its  Ante- 
cedent, I  do  not  see  how  we  can  get  from  these  two  Major  Premises  any 
really  new  Moods,  that  is  to  say,  Moods  exhibiting  any  formal  difference 
from  the  four  previously  expounded.  Recognising  these  four,  however, 
would  it  not  be  well  to  make  the  names  '  Constructive '  and  '  Destruc- 
tive •  not  synonymous  with  Modus  ponens  and  Modus  tollens  respectively, 
but  applicable  thus :  *  Constructive '  to  that  form  of  the  Modus  ponens 
that  has  an  affirmative  Conclusion,  and  '  Destructive  '  to  the  other  three 
Syllogisms  that  conclude  in  the  negative  ? 

It  must  be  carefully  observed  that,  given  the  Hypothetical 
Major  Premise — 

If  A  is  B,  C  is  D— 

we  cannot  by  denying  the  Antecedent  infer  a  denial  of  the 
Consequent.  That  A  is  B,  is  a  mark  of  C  being  D  ;  but  we  are 
not  told  that  it  is  the  sole  and  indispensable  condition  of  it.  If 
men  read  good  books,  they  acquire  knowledge ;  but  they  may 
acquire  knowledge  by  other  means,  as  by  observation.  For 
the  same  reason,  we  cannot  by  affirming  the  Consequent  infer 
the  affirmation  of  the  Antecedent :  Caius  may  have  acquired 
knowledge ;  but  we  cannot  thence  conclude  that  he  has  read 
good  books. 


124      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

To  see  this  in  another  light,  let  us  recall  chap.  v.  §  4,  where  it 
was  shown  that  a  Hypothetical  Proposition  may  be  translated  into 
a  Categorical  one;  whence  it  follows  that  a  Hypothetical  Syllogism  may 
be  translated  into  a  Categorical  Syllogism.  Treating  the  above  examples 
thus,  we  find  that  the  Modus  poncns  takes  the  form  of  Barbara,  and  the 
Modus  tollens  the  form  of  Camestres  : 

Modus  ponens.  Barbara. 

If  A  is  B,  C  is  D  ;  The  case  of  A  being  B  is  a  case  of  C  being  D  : 
A  is  B  :  This  is  a  case  of  A  being  B  : 

.-.   C  is  D.  .-.   This  is  a  case  of  C  being  D. 

Now  if,  instead  of  this,  we  affirm  the  Consequent,  to  form  the  new  Minor 

Premise, 

This  is  a  case  of  C  being  D, 

there  will  be  a  Syllogism  in  the  Second  Figure  with  two  affirmative 
premises,  and  therefore  the  fallacy  of  Undistributed  Middle.     Again  : 

Modus  tollens.  Camestres. 

If  A  is  B,  C  is  D  ;  The  case  of  A  being  B  is  a  case  of  C  being  D  ; 

C  is  not  D  :  This  is  not  a  case  of  C  being  D  : 

.'.   A  is  not  B.  .'.  This  is  not  a  case  of  A  being  B. 

But  if,  instead  of  this,  we  deny  the  Antecedent,  to  form  the  new  Minor 

Premise, 

This  is  not  a  case  of  A  being  B, 

there  arises  a  Syllogism  in  the  First  Figure  with  a  negative  Minor 
Premise,  and  therefore  the  fallacy  of  Illicit  Process  of  the  Major 
Term. 

By  thus  reducing  the  Hypothetical  Syllogism  to  the  Categorical  form, 
what  is  lost  in  elegance  is  gained  in  intelligibility.  For,  first,  we  may 
justify  ourselves  in  speaking  of  the  Hypothetical  Premise  as  the  Major, 
and  of  the  Categorical  Premise  as  the  Minor ;  since  in  the  Categorical 
form  they  contain  respectively  the  Major  and  Minor  Terms.  And, 
secondly,  we  may  justify  ourselves  in  treating  the  Hypothetical  Syllogism 
as  a  kind  of  Mediate  Inference,  in  spite  of  the  fact  that  in  the  Hypo- 
thetical Syllogism  there  are  not  two  Terms  compared  by  means  of 
a  third ;  since  in  the  Categorical  form  such  Terms  distinctly  appear  :  a 
new  Term  ('  This')  emerges  in  the  position  of  the  Minor  ;  the  place  of  the 
Middle  is  filled  by  the  Antecedent  of  the  Major  Premise  in  the 
Modus  poncns,  and  by  the  Consequent  in  the  Modus  tollens. 

In  fact,  the  mediate  element  of  the  inference  in  a  Hypothetical 
Syllogism  consists  in  asserting,  or  denying,  the  fulfilment  of  a  given 
condition.     In  the  Hypothetical  Proposition, 

If  A  is  B.  C  is  D, 
the  Antecedent,  A  is  B,  is  the  conditio  sufficiens,  or  mark,  of  the  Conse- 
quent, C  is  D ;  and  therefore  the  Consequent,  C  is  D,  is  a  conditio  sine 


1 


CONDITIONAL   SYLLOGISMS  125 

qua  non  of  the  antecedent,  A  is  B;  and  it  is  by  means  of  affirming  the 
former  condition,  or  else  denying  the  latter,  that  a  conclusion  is 
rendered  possible.  Indeed,  we  need  not  say  that  the  element  of 
mediation  consists  in  affirming,  or  denying,  the  fulfilment  of  a  given  con- 
dition :  It  is  enough  to  say  'in  affirming.'  For  thus  to  explain  the 
Modus  tollens.  reduce  it  to  the  Modus  ponens  (contrapositing  the  Major) : 

Celarent. 

If  A  is  B,  C  is  D  :  The  case  of  C  not  being  D  is  a  case 

.-.    It  C  IS  not  D,  A  is  not  B  ;  of  A  not  being  B  ; 

C  is  not  D  :  This  is  a  case  of  C  not  being  D  : 

•'•   ^  ^^  "°^  ^-  •".   This  is  a  case  of  A  not  being  B. 

The  above  four  forms  commonly  treated  of  as  Hypothetical 
Syllogisms,  are  called  by  Ueberweg  and  Dr.  Keynes  'Hypo- 
thetico-Categorical.'  Ueberweg  restricts  the  name  'Hypo- 
thetical '  simply  (and  Dr.  Keynes  the  name  *  Conditional ')  to 
such  Syllogisms  as  the  following,  having  two  Hypothetical 
Premises  : 

IfCis  D,  EisF; 
If  A  is  B,  C  is  D : 
.'.  If  A  is  B,  E  is  F. 

If  we  recognise  Particular  Hypothetical  Propositions  (see 
chap.  V.  §  4),  it  is  obvious  that  such  Syllogisms  may  be 
constructed  in  all  the  Moods  and  Figures  of  the  Categorical 
Syllogism;  and  of  course  they  may  be  translated  into^'cate- 
goricals.  We  often  reason  in  this  hypothetical  way.  For 
example  : 

If    the    margin    ot    cultivation    be    extended,    rents    will 
rise; 

If  prices  of  produce  rise,  the  margin  of  cultivation  will  be 
extended. 
.-.  If  prices  of  produce  rise,  rents  will  rise. 

But  it  may  be  noticed  that  the  purpose  of  the  Hypothetical 
Syllogism  (commonly  so  called),  as  also  of  the  Disjunctive  (to 
be  discussed  in  the  next  section)  is  to  get  rid  of  the  conditional 
element  and  obtain  a  decisive  Categorical  Conclusion ;  whereas 
these  Syllogyisms  with  two  Hypothetical  Premises,  leave  us  still 
with  a  Hypothetical  Conclusion.     This  circumstance  seems  to 


126      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

me  to  ally  them  more  closely  with  Categorical  Syllogisms  than 
with  those  that  are  discussed  in  the  present  chapter ;  they  are 
Categoricals  in  disguise:  and,  accordingly,  in  applying  the 
name  '  Hypothetical  Syllogism,'  I  have  not  seen  fit  to  depart 
from  the  older  usage.  ^  . 

§  2.  A  Disjunctive  Syllogism  consists  of  a  Disjunctive  Major 
Premise,  a  Categorical  Minor  Premise,  and  a  Categorical  Con- 
clusion. •     1  •  J 

How  many  Moods  are  to  be  recognised  in  this  kmd  of 
argument  depends  on  whether  the  alternatives  of  the  Dis- 
junctive Premise  are  regarded  as  mutually  exclusive  or  possibly 
coincident.  In  saying  '  Either  A  is  B,  or  C  is  D,'  do  we  mean 
'  either,  but  not  both,'  or  '  either,  it  may  be  both '  ?  (See  chap.  v. 

When  the  alternatives  of  the  Disjunctive  are  not  exclusive, 

we  have  only  the 

Modus  tollendo  pofiens. 

Either  A  is  B,  or  C  is  D ; 

A  is  not  B  (or  C  is  not  D) : 
/.  C  is  D        (A  is  B). 
Either  wages  fall,  or  the  weaker  hands  are  dismissed ; 
Wages  do  not  fall : 
.-.  The  weaker  hands  are  dismissed. 

But  we  cannot  argue — 
Wages  fall : 
/.  The  weaker  hands  are  not  dismissed ; 
since  in  '  hard  times '  both  events  may  happen  together. 

Rule  of  the  Modus  tollendo  ponens :  If  one   alternative   is 

denied,  the  other  is  affirmed. 

When,   however,   the  alternatives   of   the   Disjunctive  are 
mutually  exclusive,  we  have  also  the 

Modus  ponendo  tollens. 
Either  A  is  B,  or  C  is  D ; 

AisB;       (orCisD): 
.-.  C  is  not  D  (A  is  not  B). 


CONDITIONAL   SYLLOGISMS  127 

Either  the  Tories  or  the  Whigs  win  the  election ; 
The  Tories  win : 
.'.  The  Whigs  do  not  win. 

We  may  also,  of  course,  argue  as  above  in  the  Modus  tollendo  ponens— 

The  Tories  do  not  win  : 
.*.  The  Whigs  do. 
In  this  case,  to  make  the  Modus  tollendo  ponens  materially  valid,  it  must 
be  impossible  that  the  election  should  result  in  a  tie.  The  danger 
of  the  Disjunctive  proposition  is  that  the  alternatives  may  not,  between 
them,  exhaust  the  possible  cases.  Only  contradictory  alternatives  are 
sure  to  cover  the  whole  ground. 

Rule  of  the  Modus  ponendo  tollens  :  If  one  alternative  of  the  Disjunctive 
be  affirmed,  the  other  is  denied. 

Since  a  Disjunctive  Proposition  may  be  turned  into  a  Hypothetical 
Proposition  (chap.  v.  §  4),  a  Disjunctive  Syllogism  may  be  turned  into 
a  Hypothetical  Syllogism : 

Modus  tollendo  ponens.  Modus  ponens. 

Either  A  is  B  or  C  is  D ;  If  A  is  not  B,  C  is  D  ; 
A  is  not  B  :  A  is  not  B : 

•••   CisD.  ...   CisD. 

Similarly  the  Modus  ponendo  tollens  is  equivalent  to  that  kind  of  Modus 
ponens  that  may  be  formed  with  a  negative  Major  Premise;  for  if 
the  alternatives  of  a  Disjunctive  proposition  be  exclusive,  the  corre- 
sponding Hypothetical  may  be  affirmative  or  negative : 

Modus  ponendo  tollens.  Modus  ponens. 

Either  A  is  B,  or  C  is  D  ;  If  A  is  B,  C  is  not  D ; 
A  is  B  :  A  is  B  ; 

.'.   C  is  not  D.  .-.   C  is  not  D. 

Hence,  finally,  a  Disjunctive  Syllogism  being  equivalent  to  a  Hypo- 
thetical, and  a  Hypothetical  to  a  Categorical ;  a  Disjunctive  is  equiva- 
lent and  reducible  to  a  Categorical.  It  is  a  form  of  Mediate  Inference 
in  the  same  sense  as  the  Hypothetical  Syllogism  is ;  that  is  to  say,  the 
Conclusion  depends  upon  an  affirmation,  or  denial,  of  the  fulfilment  of 
a  condition  implied  in  the  Disjunctive  Major  Premise. 

§  3.  The  Dilemma  is  perhaps  the  most  popularly  interesting 
of  all  forms  of  proof.  It  is  a  favourite  weapon  of  orators  and 
wits ;  and  "  impaled  upon  the  horns  of  a  dilemma  "  is  a  painful 
situation  in  which  every  one  delights  to  see  his  adversary. 
It  seems  to  have  been  described  by  Rhetoricians  before  finding 
its  way  into  works  on  Logic;  and  Logicians,  to  judge  from 


i  I 


128      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

their  diverse  ways  of  defining  it,  have  found  some  difficulty  in 
making  up  their  minds  as  to  its  exact  character. 

There  is  a  famous   Dilemma  employed  by   Demosthenes, 
from   which   the   general   nature   of   the   argument    may   be 

gathered : 

If  ^.schines  joined  in  the  public  rejoicings,  he  is  inconsis- 
tent ;  if  he  did  not,  he  is  unpatriotic : 
But  either  he  joined,  or  he  did  not  join : 
Therefore,  he  is  either  inconsistent  or  unpatriotic. 
That  is,  reduced  to  symbols  : 

If  A  is  B,  CisD;  and  if  E  is  F,  G  is  H  :  ^ 
But  either  A  is  B,  or  E  is  F :  ^ 

:.  Either  C  is  D  or  G  is  H  {Complex  Constructive). 
Now,  plainly,  this  is  a  compound  Conditional    Syllogism, 
which  may  be  analysed  as  follows  : 

Either  A  is  B  or  E  is  F. 
Suppose  that  E  is  not  F :  Suppose  that  A  is  not  B : 

Then  A  is  B.  Then  E  is  F. 

But  if  A  is  B,  C  is  D;  But  if  E  is  F,  G  is  H; 

(AisB):  (EisF:) 

.-.  C  is  D.  .-.  G  is  H. 

.•  Either  C  is  D  or  G  is  H. 
A  Dilemma,  then,  is  a  compound  Conditional  Syllogism, 
having  for  its  Major  Premise  two  Hypothetical  Propositions, 
and  for  its  Minor  Premise  a  Disjunctive  Proposition,  whose 
ahernative  Terms  either  affirm  the  Antecedents  or  deny  the 
Consequents  of  the  two  Hypothetical  Propositions  forming  the 

Major  Premise. 

The  Hypotheticals  in  the  Major  Premise,  may  have  all  four 
Terms  distinct  (as  in  the  above  example) ;  and  then  the  Con- 
clusion is  a  Disjunctive  Proposition,  and  the  Dilemma  is  said 

to*  be  Complex. 

Or  the  two  Hypotheticals  may  have  a  common  Antecedent 
or  a  common  Consequent;  and  then  the  Conclusion  is  a 
Categorical  Proposition,  and  the  Dilemma  is  said  to  be 
Simple, 


CONDITIONAL  SYLLOGISMS  129 

Again,  the  alternatives  of  the  Disjunctive  Minor  Premise 
may  be  Affirmative  or  Negative.  If  Affirmative,  the  Dilemma 
IS  called  Constructive ;  and  if  Negative,  Destructive.  However, 
seeing  that  the  Dilemma  is  a  compound  Conditional  Syllogism' 
It  would  surely  be  better  to  name  its  Moods  after  the  cor- 
responding Moods  of  the  Hypothetical  Syllogism— i^^^/^i- 
ponens  and  Modus  tolleus. 

If,  then,  we  use  only  affirmative  Hypotheticals  in  the  Major 
Premise,  there  are  four  Moods  : 

I.  The  Simple  Modus  ponens  (or,  Constructive). 

If  AjsJ,  C  is  D;  and  if  E  is  F,  C  is  D : 

But  either  A  is  B,  or  E  is  F: 
.-.  C  is  D. 

If  the  Tories  win  the  election,  the  Government  will  avoid 
innovation ;  and  if  the  Whigs  win,  the  House  of  Lords 
will  prevent  them  innovating : 
But  either  the  Tories  or  the  Whigs  will  win  ; 
.'.  Innovation  is  improbable. 
2.  The  Complex  Modus  pone?is  (or,  Constructive). 
IfAisB^CisD:  andifE^F,  GisH: 

But  either  A  is  B,  or  eITF: 
.-.  Either  C  is  D,  or  G  is  H. 
If  Appearance  is  all  that  exists.  Reality  is  a  delusion ;  and 
if  there   is   a   Substance   beyond  Consciousness,  Know- 
ledge of  Reality  is  impossible  : 
But  either  Appearance  is  all,  or  there  is  a  Substance  beyond 
Consciousness : 
.-.  Either  Reality  is  a  delusion,  or  a  knowledge  of  it  is  im- 
possible. 
3.  Simple  Modus  tollens  (or  Destructive). 

If  A  is  B,  C  is  D;  and  if  A  is  B,  E  is  F : 

But  either  C  is  not  D,  or  E  is  not  F : 
.'.  A  is  not  B. 
If  table-rappers  are  to  be  trusted,  the  departed  are  spirits; 
and  they  also  exert  mechanical  energy : 


I30      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

But   either   the   departed   are  not  spirits,  or   they   do    not 
exert  mechanical  energy : 
.'.  Table-rappers  are  not  to  be  trusted. 
4.  Complex  Modus  tollens  (or,  Destructive). 

If  A  is  B,  C  is  D ;  and  if  E  is  F,  (;  is  H : 

But  either  C  is  not  D,  or  G  is  not  H : 
.-.  Either  A  is  not  B,  or  E  is  not  F. 
If  poetic  justice  is  observed,  virtue  is  rewarded ;  and  if  the 

mirror  is  held  up  to  Nature,  the  villain  triumphs  : 
But  either  virtue  is  not  rewarded,  or  the  villain  does  not 

triumph : 
/.  Either  poetic  justice  is  not  observed,  or  the  mirror  is  not 

held  up  to  Nature. 

These  then  are  the  four  Moods  of  the  Dilemma  that  emer-e  if  we  use 
only  affirmative  Hypothetical  for  the  Major  Premise  ;  but.  certainly  it 
is  often  quite  as  natural  to  employ  two  negative  Hypotheticals  (indeed 
one  might  be  affirmative  and  the  other  negative ;  but  waive  that) ;  and 
then  four  more  Moods  emerge,  all  having  negative  Conclusions.     But 
it  is  needless  to  intimidate  the  reader  by  drawing  up  these  four  Moods 
in  battle  array.     Of  course,  they  always  admit  of  reduction  to  the  fore- 
going  Moods  by  obverting  the  Hypotheticals ;  but  by  the  same  process 
we  may  greatly  decrease   the  number   of  Moods  of  the  Categorical 
Syllogism ;    so  that  I  am  afraid  that  this  objection  to  them  will  be 
thought  to  prove  too  much.     Just  as  some  Syllogisms  are  most  simply 
expressed  in  Celarent  or  Cesare,  so  some  Dilemmas  are  most  simply 
stated  with  negative  Major  Premises-^.^'.  :     The  simple  Modus  Poncns 
above  given  would   run  more  naturally  thus:   //  the  Tories  win,  the 
Government  will  not  innovate;  and  if  the  Whigs,  the  Lords  will  not  let  them  : 
and  similarly  Demosthenes'  Dilemma— 7/  JEschines  joined,  he  ts  not  con- 
sistent: and  if  he  did  not,  he  is  not  patriotic.     Moreover,  the  propriety  of 
recognising  Dilemmas  with  negative  Major  Premises,  follows  from  the 
above  analysis  of  the   Dilemma  into  a  combination  of  Hypothetical 
Syllogisms,  even  if  (as  in  §  i  of  this  chapter)  we  take  account  of  only 
four  Moods  of  the  Hypothetical  Syllogism. 

In  the  rhetorical  use  of  the  Dilemma,  it  may  be  observed  that  the 
Disjunction  in  the  minor  premise  ought  to  be  ob\-ious,  or  (at  any  rate) 
easily  acceptable  to  the  audience.  Thus.  Either  the  Tories  or  the  Whigs 
will  win ;  Either  ALschines  joined  in  the  rejoicings,  or  he  did  not;  such  propo- 
sitions are  not  likely  to  be  disputed.  But  if  the  orator  must  stop  to 
prove  his  Minor  Premise,  the  smacking  effect  of  this  figure  (if  the 
expression  be  allowed)  will  be  lost.     Hence  the  Minor  Premises  of 


CONDITIONAL  SYLLOGISMS 


stde^ntToTSlf  ^t\  ''  ^-  ^  -^-t  audience,  ^ 

mechanical  ..^r  .^^^Tl^^ :;" ^'\  ^.^  ''  ""''  ''''' 
taught   by  physical  philosophers    7h!^       t  P^^"^^?^^.   generally 

energy;  and  that  £.L    jf  ^^^^^  ^^  ^^e  vehicle  of 

consciousness,  is  a  doctrine  whtl!      1  '  ''  ^^''''  ''  ^  ^"^^^^^^^  ^^yond 

be   expected    to   tde  sta^d^  metaphysical  philosophers  could 

expected  to  agree      Hot'^^^^^  "pon    which    they    could    not    be 

junction  may  not'be  reX        t   ^    ^^  ^""^''  ^'  ^^^*  ^  P^^^^^^le  dis- 

does  not  allow  fo^a  ^eZ ^:::::z^::i  SiS:^'  -  '^rr 

resistance  would  be  vain  •  x.^f        1,         /  ^      ^  movement  where 

sistent  with  subse'uenTcon'  ra'o~  or.h^  "  "f  ""'  "^  '"^- 
patible  with  patriotic  reserve  Zd  "on  a  taeTth::';":","""'-'"^"™- 
premature  and  ominous  ^^  rejoicings  are 

way,  sho„M  ^^::^l^!::s:^^'77:^^::^''^''-'-- 

sistent  or  unpatriotic  ■ :  horrid  words  to  a  poiuldan'  •  Eitt  '",°"" 

or  no  possible  knowledge  ■  ■  very  disaDnoinHno.  *      '  "°  ""^^'"y 

Thus  the  Disjunctive  Conclu'on  'sTC  lo     .?  ""°"'  """""^  ' 
Categorical  one  in  a  Simple  Dilemma  °PP°"'"'  ^^   *'^ 

Logicians  further  speak  of  the  Trilemma,  with  three  Hyno 
thetcals  and  a  corresponding  triple  Disjunction;  and  of  a 
Polylemma,  w,th  any  further  number  of  perplexities.  But  any 
one  who  has  a  taste  for  mere  logical  forms  may  haye  it  a L p  ' 
gratified  m  numerous  text-books.  Indeed  there  are  so  Zy 
opportun,t,es  of  deyeloping  such  forms  that,  if  i  "e'ioZ 
enough,  a  .nan  may  still  hope  to  discoyer  some  quUe  "  w 
one.  and  qu.te  „,„ocently,  as  long  as  he  does  n't  pu.^  ^ 


1 


TRANSITION  TO  INDUCTION 


CHAPTER  XIII 
TRANSITION   TO   INDUCTION 

§  I.  Having  now  discussed  Terms,  Propositions,  Immediate 
and  Mediate  ^Inferences,  and  investigated  the  conditions  of 
Formal  Truth  or  Consistency,  we  have  next  to  consider  the 
conditions    of  Material   Truth :    whether   (or   how  far)    it  is 
possible  to  arrive  at  propositions  that  represent  the  course  of 
nature  and  human  life.     Hitherto  we  have  dealt  with  no  sort 
of  proof  that  gives  any  such  assurance.     A  valid  Syllogism 
guarantees  the  truth  of  its  Conclusion,  provided  the  Premises 
be  true :  but  what  of  the  Premises  ?     The  relation  between 
the  Premises  of  a  valid  Syllogism  and  its  Conclusion  is  indeed 
the  same  as  the  relation  between  the  Antecedent  and  Conse- 
quent of  a  Hypothetical  Proposition.      If  A  is  B,  C  is  D  : 
grant  that  A  is  B,  and  it  follows  that  C  is  D  ;  and,  similarly, 
grant  the  Premises  of  a  Syllogism,  and  the  Conclusion  follows. 
Again,  grant  that  C  is  not  D,  and  it  follows  that  A  is  not  B  ; 
and,  similarly,  if  the  Conclusion  of  a  valid  Syllogism  be  false, 
it  follows  that  one,  or  other,  or  both  of  the  Premises  must  be 
false,  or  else  that  they  are  illicitly  connected.     But,  once  more, 
grant  that  C  is  D,  and  it  does  not  follow  that  A  is  B  ;    so 
neither,  if  the  Conclusion  of  a  Syllogism  be  true,  does  it  follow 
that  the  Premises  are.     For  example  :— 

Geology  is  an  exact  science ; 
Mathematics  is  a  branch  of  Geology ; 
. .    Mathematics  is  an  exact  science. 
Here  the  conclusion  is  true  although  the  Premises  are  absurd. 
Or  again  : — 


f 


^33 


Mathematics  is  an  exact  science ; 
Geology  is  a  branch  of  Mathematics  : 
.*.  Geology  is  an  exact  science. 
Here  the  Major  Premise  is  true,  but  the  Minor  is  false,  and  the 
Conclusion  is  false.     In  both  cases,  however,  whether  the  Con- 
clusion be  true  or  false,  it  equally  follows  from  the  Premises,  if 
there  is  any  cogency  in  Barbara.     The  explanation  of  this  is 
that  Barbara  has  only  formal  cogency ;  and  that  whether  the 
conclusion  of  that,   or  any  other  valid  Mood,  shall  be  true 
according  to  fact  and  experience,  depends  upon  how  the  form 
is  filled  up.     How  to  establish  the  Premises,  then,  is  the  most 
important  problem ;  and  it  still  remains  to  be  solved. 

§  2.  We  may  begin  by  recalling  the  distinction  between  the 
Denotation  and  Connotation  of  a  General  Term  :  the  Denota- 
tion comprising  the  things  or  events  which  the  Term  is  a  name 
for;    the  Connotation   comprising   the  common  qualities  on 
account  of  which  these  things  are  called  by  the  same  name. 
Obviously,  there  are  very  few  General  Terms  whose  denotation 
is  exhaustively  known  ;  since  the  denotation  of  a  General  Term 
comprises  all  the  things  that  have  its  connotation,  or  that  ever 
have  had,  or  that  ever  will  have  it,  whether  they  exist  here,  or 
in  Australia,  or  in  the  Moon,  or  in  the  utmost  stars.     No  one 
has  examined  all  men,  all  dogs,  all  falling  bodies,  all  cases  of 
fever,  all  crystals,  all  mammoths,  all  revolutions,  all  stars— nor 
even  all  planets,  since  from  time  to  time  new  ones  are  discerned. 
We  have  names  for  animals  that  existed  long  before  there  were 
men  to  observe  them,  and  of  which  we  know  only  a  few  bones 
the  remains  of  multitudinous  species:  others  may  continue  to 
exist  when  men  have  disappeared  from  the  earth. 

If,  indeed,  we  definitely  limit  the  time,  or  place,  or  quantity 
of  matter  to  be  explored,  we  may  sometimes  learn,  within  the 
given  limits,  all  that  we  are  concerned  about :  as  all  the  bones 
of  a  paiticular  animal,  or  the  list  of  English  monarchs  hitherto 
or  the  names  of  all  the  members  of  the  House  of  Commons 
at  the  present  time.  Such  cases,  however,  do  not  invalidate 
the  above  logical  truth  that  few  General  Terms  are  exhaustively 


I 


,34      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

known  in  their  denotation ;  for  the  very  fact  of  assigning  limits 
of  time  and  place  impairs  the  generality  of  a  Term.  Ihe 
bones  of  a  certain  animal  may  be  all  examined,  but  not  the 
bones  of  all  animals,  nor  even  of  one  species.  The  English 
monarchs  that  have  reigned  hitherto  may  be  known,  but  there 

may  be  many  still  to  reign. 

The    General   Terms,   then,   with   which   Logic   is   chiefly 
concerned,  the  names  of  Causes  and  Kinds,  such  as  gravita- 
tion, diseases,    social   events,    minerals,    plants   and   animals, 
sfand  for  some  facts  that  are,  or  have  been,  known,  and  for  a 
great  many  other  similar  ones  that  have  not  been,  and  never 
will  be,  known.     Hence  the  use  of  a  General  Term  depends 
not  upon  our  direct  knowledge  of  everything  comprised  in  its 
denotation,  but  upon  our  readiness  to  apply  it  to  anything 
that  has  its  connotation,  whether  we  have  seen  the  thing  or  not, 
and  even  though  we  never  can  see  it ;  as  when  a  man  talks 
freely  of  the  ichthyosaurus,  or  of  the  central  heat  of  planets,  or 

of  atoms  and  ether.  , 

Hence    Universal   Propositions,  which   consist   of  General 
Terms,   deceive  us,  if  we  suppose  that   their  predicates  are 
directly  known  to  be  related  to  all  the  facts  denoted  by  their 
subjects.     In  exceptional  cases,  in  which  the  denotation  of  a 
subject  is  intentionally  limited,  such  exhaustive  direct  know- 
ledge may  be  possible  ;   as  that  "  all  the  bones  of  a  certain 
animal  consist  of  phosphate  of  lime,"  or  that  every  member  of 
the  present  Parliament   wears   a   black   silk   hat.     But  what 
predication  is  possible  concerning  the  hats  of  all  members  of 
Parliament  from  the  beginning?     Ordinarily,  then,  whilst  the 
relation  of  predicate  to  subject  has  been  observed  in  some 
cases,  in  much  the  greater  number  of  cases  our  belief  about  it 
depends  upon  other  evidence  than  observation,  or  may  be  said 
(in  a  certain  sense)  to  be  taken  on  trust. 

'  All  rabbits  are  herbivorous ' :  why  do  we  believe  that  ? 
We  may  have  seen  a  few  wild  rabbits  feeding ;  or  have  kept 
tame  ones,  and  tried  experiments  with  their  diet ;  or  have  read 
of  their  habits  in  a  book  of  Natural  History  ;  or  have  studied 


I 

r 


TRANSITION   TO   INDUCTION  135 

the  physiology  of  digestion  in  many  sorts  of  animals  :  but  with 
whatever  care  we  add  testimony  and  scientific  method  to  our 
own  observation,  it  still  remains  true  that  the  rabbits  observed 
by  ourselves  and  others  are  few  in  comparison  with  those  that 
live,  have  lived  and  will  live.  And  the  same  truth  might 
be  shown  to  hold  good  of  any  other  General  Proposition  ; 
for  it  plainly  follows  from  the  fact  that  the  General  Terms 
of  which  such  propositions  consist,  are  never  exhaustively 
known  in  their  denotation.  What  right  have  we  then  to  state 
Universal  Propositions  ?  That  is  the  problem  of  Inductive 
Logic. 

§  3.  Universal  Propositions,  of  course,  cannot  always  be 
proved  by  Syllogisms;  because  to  prove  an  Universal  Pro- 
position^ by  a  Syllogism,  its  premises  must  be  Universal 
Propositions ;  and,  then,  these  must  be  proved  by  others,  and 
so  on  for  ever.  In  fact  the  Formal  Syllogism  is  itself  mis- 
leading, if  the  Universal  Proposition  is  so :  if  we  think  that 
the  premises  prove  the  conclusion  because  they  have  been 
established  by  detailed  observation,  we  are  mistaken.  The 
consideration  of  any  example  will  show  this.  Suppose  any 
one  to  argue  : 

All  ruminants  are  herbivorous  ; 

Camels  are  ruminants : 
.*.  Camels  are  herbivorous. 
Have  we,  then,  examined  all  ruminants?  If  so,  we  must 
have  examined  all  camels,  and  cannot  need  a  syllogism  to 
prove  their  herbivorous  nature  :  instead  of  the  Major  Premise 
proving  the  Conclusion,  the  Conclusion  must  then  be  part  of 
the  proof  of  the  Major  Premise.  But  if  we  have  not  examined 
all  ruminants,  having  omitted  most  giraffes,  most  deer,  most 
camels,  how  do  we  know  that  the  unexamined  (say,  some 
camels)  are  not  exceptional  ?  Camels  are  vicious  enough  to  be 
carnivorous  ;  and  indeed  it  is  said  that  Bactrian  camels  will 
eat  flesh  rather  than  starve,  though  of  course  their  habit  is 
herbivorous. 

Or,  again,  it  is  sometimes  urged  that — 


136      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

All  empires  decay : 
.'.  Britain  will  decay. 
This  is  manifestly  a  prediction  :  at  present  Britain  flourishes, 
and  shows  no  signs  of  decay.  Vet  a  knowledge  of  its  decay 
seems  necessary,  to  justify  any  one  in  asserting  the  given 
premise.  If  it  is  a  question  whether  Britain  will  decay,  to 
attempt  (whilst  several  empires  still  flourish)  to  settle  the 
matter  by  asserting  that  all  empires  decay,  seems  to  be  '  a 
begging  of  the  question.'  But  although  this  case  is  a  manifest 
prediction,  it  does  not  really  diff^er  from  the  last  one  ;  for 
the  proof  that  camels  are  herbivorous  has  no  limits  in  time. 
If  valid,  it  shows  not  only  that  they  are,  but  also  that  they 
will  be,  herbivorous. 

Hence,  to  revert  to  a  dilemma,  it  may  be  urged :  If  aU  the 
facts  of  the  Major  Premise  of  any  Syllogism  have  been  examined, 
the  Syllogism  is  needless ;  and  if  some  of  them  have  not  been 
examined,  it  is  a  petltio  principii.  But  either  all  have  been  ex- 
amined, or  some  have  not.  Therefore,  the  Syllogism  is  either 
useless  or  fallacious. 

§  4.  A  way  of  escape  from  this  dilemma  is  provided,  how- 
ever, by  distinguishing  between  the  formal  and  material 
aspects  of  the  Syllogism  considered  as  a  means  of  proof.  It 
begs  the  question  formally,  but  not  materially ;  that  is  to  say, 
if  it  be  a  question  whether  camels  are  herbivorous,  and  to 
decide  it  we  are  told  that  'all  ruminants  are,'  laying  stress 
upon  the  'all,'  as  if  all  had  been  examined,  though  in  fact 
camels  have  not  been,  then  the  question  as  to  camels  is 
begged.  The  form  of  an  universal  proposition  is  then  offered 
as  evidence,  when  in  fact  the  evidence  has  not  been  universally 
ascertained.  But  if  in  urging  that  '  all  ruminants  are  herb- 
ivorous '  no  more  is  meant  than  that  so  many  other  ruminants 
of  diff'erent  species  are  known  to  be  herbivorous,  and  that  the 
ruminant  stomach  is  so  well  adapted  to  a  coarse  vegetable 
diet,  that  the  same  habit  may  be  expected  in  other  ruminants, 
such  as  camels,  the  argument  then  rests  upon  material 
evidence   without   unfairly   implying    the    case    in    question. 


TRANSITION   TO   INDUCTION 


137 


4 


• 


' 


Now  the  nature  of  the  material  evidence  is  plainly  this,  that 
the  resemblance  of  camels  to  deer,  oxen,  etc.^  in  the  fact  of 
chewing  the  cud,  justifies  us  in  believing  that  they  have  a 
further  resemblance  in  the  fact  of  feeding  on  herbs ;  in  other 
words,  we  assume  that  7'esemblance  is  a  ground  of  inference. 

Another  way  of  putting  this  difficulty  with  regard  to  syllo- 
gistic evidence,  which  we  have  just  been  discussing,  is  to 
object  that  by  the  Laws  of  Syllogism  a  Conclusion  must  never 
go  beyond  the  Premises,  and  that  therefore  no  progress  in 
knowledge  can  ever  be  established,  except  by  direct  observa- 
tion. Now,  taking  the  Syllogism  formally,  this  is  true  :  if  the 
Conclusions  go  beyond  the  Premises,  there  must  be  either  four 
Terms,  or  illicit  process  of  the  Major  or  Minor  Term.  But 
taking  it  materially,  the  Conclusion  may  cover  facts  which 
were  not  in  view  when  the  Major  Premise  was  laid  down ; 
facts  of  which  we  predicate  something  not  as  the  result  of 
direct  observation,  but  because  they  resemble  in  a  certain  way 
those  facts  which  had  been  shown  to  carry  the  predicate  when 
the  Major  Premise  was  formed. 

*What  sort  of  resemblance  is  a  sufficient  ground  of  in- 
ference ? '  is,  therefore,  the  important  question  alike  in  material 
Deduction  and  in  Induction  ;  and  we  shall  presently  endeavour 
to  answer  it.  In  the  above  cases,  the  fact  of  chewing  the  cud 
is  a  strong  ground  for  inferring  vegetarianism  ;  the  resemblance 
of  Britain  to  other  empires  is  a  much  less  substantial  basis  for 
expecting  her  ultimate  downfall. 

§  5.  If,  now,  the  material  character  of  syllogistic  proof  is 
such  as  we  have  above  described,  in  order  to  generalise  it  the 
axiom  de  onini  et  nullo  needs  to  be  restated.  "That  whatever 
is  true  of  a  whole  class  is  true  of  everything  the  class  includes," 
seems  from  our  present  point  of  view  to  be  a  dictum  designed 
to  justify  the  begging  of  the  question.  That  whatever  is  true 
of  all  is  true  of  some,  is  a  merely  formal  subaltern  inference  : 
knowing  'all,'  how  can  there  be  any  question  about  the 
*  some '  ?  But  if  we  do  not  know  '  all,'  not  really  the  '  whole 
class,'  we  must  write  the  dictum  thus  :    Whatever  we  have  reason 


\ 


138      LOGIC:    DEDUCTIVE  AND   INDUCTIVE 

to  regard  as  constantly  connected  ivith  the  nature  or  connotation 
of  a  class  or  class-name,  we  may  expect  to  be  similarly  connected 
with  whatever  can  be  shoivn  to  have  that  nature  or  connotation. 
Thus  the  feeding  upon  herbage,  being  connected  with  the 
nature  of  ruminants,  is  connected  with  camels,  because  they 

ruminate. 

Another  way  of  putting  this  principle  \^—Nota  notcB,  nota 
ret  ipsius,  '  the  mark  of  a  mark  is  a  mark  of  the  thing  itself,'  or 
*  whatever  has  a  mark  has  what  it  is  a  mark  of.'  A  mark  is 
anything  (A)  that  is  never  found  without  something  else  (B)  \ 
so  that  where  we  find  A,  B  may  be  expected.  Now  a  camel  is  a 
mark  of  ruminating  ;  and  ruminating  is  a  mark  of  feeding  upon 
herbage  :  therefore,  a  camel  is  a  mark  of  feeding  upon  herbage. 

§  6    I  must  add  that,  as  we  distinguish  between   the  formal  and 
material  character  of  the  Syllogism,  so  we  ought  in  the  case  of  Sub- 
alternation.   To  infer  I.  from  A.  may  imply  a  real  advance  of  knowledge, 
if  the  '  Some '  of  the  I.  were  not  in  view  when  '  All '  was  attached  to  the 
subject  of  the  A.     Thus  Britain  will  decay  goes  beyond  the  material 
grounds  of  All  empires  decay,  n3.me\y.  those  known  to  have  decayed: 
nevertheless  it  is  a  subaltern  not  a  mediate  inference ;  smce  such  a 
Minor  premise  as  Britain  is  an  empire   (only  true  in  the  form-'  the 
British  empire  is  an  empire')  is  a  verbal  proposition  in  disguise,  and 
adds  nothing  to  the  argument.     If  the  inference  Britain  uill  decay  is 
doubtful  it  is  not  because  a  false  Minor  premise  has  been  omitted  by 
Enthymeme,  but  because  the   Subalternans  is  doubtful,  because   the 
empires  that  have  been  known  to  decay  may  not  be  fair  examples  of 
all  empires.     It  should  be  expressed-^//  empires  having  such  or  such 
characteristics.       There  is  then   room  for   a   real   Minor   premise-T/«^ 
British  empire  has  these  characteristics ;  and  on  whether  that  is  true,  or  not. 
depends  the  value  of  the  inference  Britain  will  decay.     Similarly,   the 
stock  example— yl//  men  are  mortal;    therefore,  Socrates  is  mortal,  is  a 
Subalternation :  for  although  the  Minor  premise.  Socrates  is  a  man,  is  a 
real  proposition  under  the  rule  that  proper  names  have  no  connotation  ; 
yet  this  rule  is  suspended  by  the  context  or  suppositio :  we  are  talking  of 


men. 


§  7.  The  Syllogism  has  sometimes  been  discarded  by  those 
who  have  only  seen  that,  as  formally  stated,  it  is  either  useless 
or  fallacious  :  but  those  who  also  perceive  its  material  grounds, 
retain  and  defend  it.     In  fact,  great  advantages  are  gained  by 


TRANSITION  TO   INDUCTION 


J  39 


i 


J 


stating  an  argument  as  a  formal  Syllogism.  For,  in  the  first 
place,  we  can  then  examine  separately  the  three  conditions  on 
which  the  validity  of  the  argument  depends  : 

(i)  Are  the  Premises  so  connected  that,  //  they  are  true,  the 
Conclusion  follows  ?  This  depends  upon  the  formal  principles 
of  chap.  X. 

(2)  Is  the  Minor  Premise  true?  This  question  can  only 
arise  when  the  Minor  Premise  is  a  real  proposition.  That 
Britain  is  an  empire  affords  no  matter  for  doubt  or  inquiry  ; 
but  whether  Britain  resembles  Egypt,  Assyria,  Rome  in  those 
circumstances  that  led  to  their  decay,  is  a  very  difficult  subject 
for  investigation.  That  Camels  are  rumitiatits  is  now  a  verbal 
proposition  to  a  Zoologist,  but  not  to  the  rest  of  us ;  and  even 
to  the  Zoologist  the  ascertaining  of  the  relation  in  which  camels 
stand  to  such  ruminants  as  oxen  and  deer,  is  not  a  matter  of 
analysing  words  but  of  dissecting  stomachs. 

(3)  Is  the  Major  Premise  true  ?  Are  all  ruminants  herbi- 
vorous ?  If  there  be  any  exceptions  to  the  rule,  camels  are 
likely  enough  to  be  among  the  exceptions.  And  here  the 
need  of  Induction  is  most  conspicuous  :  how  can  we  prove  our 
Premises  ? 

A  second  advantage  of  the  Syllogism  is,  that  it  makes  us 
fully  aware  of  what  an  inference  implies.  An  inference  must 
have  some  grounds,  or  else  it  is  a  mere  prejudice ;  but  what- 
ever the  grounds  are,  if  they  are  sufficient  in  a  particular  case, 
they  must  be  sufficient  for  all  similar  cases,  they  must  admit  of 
being  generalised ;  and  to  generafise  the  grounds  of  the  in- 
ference, is  nothing  else  than  to  state  the  Major  Premise.  If 
the  evidence  is  sufficient  to  justify  the  argument  that  camels 
are  herbivorous  because  they  are  ruminants,  it  must  also  justify 
the  Major  Premise,  All  ruminants  are  herbivorous  ;  for  else  the 
inference  cannot  really  depend  merely  upon  the  fact  of  rumi- 
nating. To  state  our  evidence  syllogistically,  then,  must  be 
possible,  if  the  evidence  is  mediate  and  of  a  logical  kind  ;  and 
to  state  it  in  this  formal  way,  as  depending  on  the  truth  of  a 
general  principle,  the  Major  Premise,  increases  our  sense  of 


I40      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

responsibility  for  the  inference  that  is  thus  seen  to  imply  so 
much;  and  if  there  are  any  negative  instances  within  our 
knowledge,  we  are  the  more  likely  to  remember  them.  The 
use  of  Syllogisms  therefore  is  likely  to  strengthen  our  reason- 
ings. 

A  third  advantage  is,  that  an  accurate  generalisation  may  be 
useful  to  others  :  it  is  indeed  part  of  the  systematic  procedure 
of  science.  The  memoranda  of  our  Major  Premises,  or  reasons 
for  believing  anything,  may  be  referred  to  by  those  who  come 
after  us,  and  either  confirmed  or  refuted.  When  such  a  memo- 
randum is  used  for  further  inferences,  these  inferences  are  said, 
in  the  language  of  Formal  Logic,  to  be  dv:x\\n  from  it,  as  if  the 
Conclusion  were  contained  in  our  knowledge  of  the  Major 
Premise ;  but,  considering  the  limited  extent  of  the  material 
evidence,  it  is  better  to  say  that  the  inference  is  drawn  accord/// 1^ 
to  the  memorandum  or  Major  Premise,  since  the  grounds  of 
the  Major  Premise  and  of  the  Conclusion  are  in  fact  the 
same. 

We  shall  see  hereafter  that  Inductive  proofs  may  be  stated 
in  Syllogisms,  and  that  Inductive  inferences  are  drawn  according 
to  the  Law  of  Causation. 

§  8.  Of  the  above  three  conditions  on  which  the  validity  of 
an  argument  depends,  namely,  (i)  its  formal  correctness  as 
a  Syllogism,  (2)  the  truth  of  the  Minor,  and  (3)  of  the  Major 
Premise,  the  most  difficult  to  ensure  are  clearly  the  second  and 
third,  and  especially  the  third.  And  here  lies  one  important 
connection  between  Deduction  and  Induction.  How  can  we 
know  whether  the  premises  of  a  Deductive  argument  are  true  ? 
By  Induction.  Sometimes,  indeed,  premises  moy  be  deduced 
by  Prosyllogisms :  All  men  are  mortal,  it  may  be  said,  because 
All  animals  are  mortal ;  and  All  animals  are  mortal,  because 
All  composite  bodies  are  subject  to  dissolution.  But  if  there  were 
no  limit  to  this  process,  proof  would  involve  a  regressus  ad 
infinitum,  for  which  life  is  too  short;  and,  besides,  con- 
venient Prosyllogisms  are  not  always  to  be  found.  Accordingly, 
Logic  accepts  certain  Principles,  Axioms,  or  ultimate  Major 


r 


TRANSITION   TO   INDUCTION 


141 


Premises,  such  as  the  Laws  of  Thought  and  Causation,  as  con- 
ditions of  all  reasoning,  leaving  it  to  Metaphysics  to  investigate 
their  grounds  ;  whilst  the  common  run  of  general  propositions, 
laws,  or  premises,  if  they  have  any  scientific  grounds,  are  either 
obtained  by  Induction  from  facts  with  the  aid  of  the  ultimate 
Axioms  and  Principles,  or  else  are  Hypotheses  (that  is,  pre- 
mises provisionally  assumed). 

For  example,  how  do  we  know  that  all  ruminants  are  herbi- 
vorous ?  We  have  only  directly  observed  that  great  multitudes 
are  so  ;  the  examination  of  a  few  specimens  shows  that  their 
organisation  is  adapted  to  a  vegetable  diet,  and  we  infer  that 
unobserved  ruminants  are  also  herbivorous,  by  assuming  that 
resemblance  (in  ruminating)  is  a  ground  of  inference  (to  the 
property  of  feeding  on  herbage).  If  you  ask.  Why  ?  the  usual 
answer  is,  *  Because  of  the  Uniformity  of  Nature.'  This  is  con- 
sidered to  be  an  ultimate  principle,  for  which  it  is  needless  and 
useless  to  ask  a  reason,  but  with  the  help  of  which  our  ordinary 
Major  Premises  may  be  obtained  by  Induction  from  facts. 
And  in  the  same  way  (as  we  saw  in  §  4)  the  conclusion  of  a 
Syllogism  is  obtained  from  the  material  evidence  embodied  in 
the  Major  Premise,  namely,  by  assuming  that  resemblance  is  a 
ground  of  inference,  or  that  Nature  is  uniform. 

§  9.  The  Uniformity  of  Nature  cannot  be  defined  and  is  there- 
fore liable  to  be  misunderstood.  In  many  ways  Nature  seems  not 
to  be  uniform  :  there  is  great  variety  in  the  sizes,  shapes,  colours 
and  all  other  properties  of  things :  bodies  falling  in  the  open 
air — pebbles,  slates,  feathers — descend  in  different  lines  and  at 
different  rates  ;  the  wind  and  weather  are  proverbially  uncertain  ; 
the  course  of  trade,  or  of  politics,  is  full  of  surprises.  Yet 
common  maxims,  even  when  absurd,  testify  to  a  popular  be- 
lief that  the  relations  of  things  are  constant :  the  doctrine  of 
St.  Swithin  and  the  rhyme  beginning  *  Evening  red  and  morning 
grey,'  show  that  the  weather  is  held  to  be  not  wholly  unpre- 
dictable ;  as  to  human  affairs,  it  is  said  that  *  a  green  Yule 
makes  a  fat  churchyard,'  that  'trade  follows  the  flag,'  and  that 
*  history  repeats  itself ' ;  and  Superstition  knows  that  witches 


142      LOGIC:   DEDUCTIVE    AND   INDUCTIVE 

cannot  enter  a  stable-door  if  a  horse-shoe  ^f  l^^.-^^^;;"^"^ 

that  the  devil  cannot  cross  a  ^^^^^^^''^^^^^^^^^^ 
pentagon.     But  the  surest  proof  of  a  belief  m  the  y-» 
If  Nature  is  given  by  the  conduct  of  men  and  an.rnals     by  tha 
adherence  to  habit,  custom  and  tradition    to  ^^^^  ^^^^^^^ 
times  they  chiefly  owe  their  safety,  but  which  wou      dai  y  d- 
appoint  and  destroy  them,  if  it  were  not  ^-^fl^lX 
thinc^s  may  be  found  where  they  have  been  left  and  that  in 
similar  circumstances  there  are  similar  events. 

Now  this  general  belief,  seldom  distinctly  conceived,  for  the 
most  part  quite  unconscious  (as  a  principle),  merely  imphed  m 
:::;  L  l,  is  also  the  foundation  of  all  the  Sci^ 
are  entirely  occupied  in  seeking  the  Laws  (that  is,  the  Un 
olities)  of  NaL.     And  Philosophy,  endeavou^^^^^ 
nature  is    to   generalise  to  the  utmost,  whilst  retaining  the 
d  ai:Jss  of'scientiac  thought,  resolves  the  -mpr^^^^^^^^^^^^^^^ 
but  indeterminate  notion  of  Uniformity  into  a  number  of  First 
Principles,  which  may  be  indicated  as  follows : 

(X)  The  Principles  of  Contradition  and  Excluded   Middle 
(i^  ti  \?  3).__These  are  called  Laws  of  Thought ;  and  so  they 
te  •  for  in  the  f^rst  place,  it  is  true  of  thoughts,  as  of  every- 
tl'c.  el'se,  that  they  have  a  certain  content  or  not ;  occur  in  a 
lel^:  order,  or  dJnot ;  and,  in  the  second  P^-,^^^^^^^^^^^^^ 
reference  to  an  object  thought  about,  is  bound  to  observe  these 
aw  son  pain  of  else  going  wrong.     But  the  reason  why  the 
Ibove  principles  are  laws  of  Thought  in  this  secondary  sense 
/tW  is  as  rules  or  imperatives)  is,  that  they  are  laws  of  things 
tV;^  of' 'laws'  (as  uniformities) ;  for  else  they 

:ould  rdirect  us,  and  it  would  be  (literally)  madness  to  con- 

'T)"certrn  Axioms  of  Mediate  Evidence:  as,  in  Mathe- 
matics '  that  magnitudes  equal  to  the  same  magnitude  are 
"  ul  to  one  another';  and,  in  Logic,  the  i^^^^-,  or  its 
I'T^M^^  the  mark  of  a  mark  is  a  mark  of  the  thing  itself. 
T)  That  all  Times  and  all  Spaces  are  commensurable.-If 
Time  really  trotted  with  one  man  and  galloped  with  another, 


TRANSITION   TO   INDUCTION 


143 


as  it  seems  to;  if  Space  really  swelled  in  places,  as  De 
Quincey  dreamed  that  it  did;  life  could  not  be  regulated, 
experience  could  not  be  compared,  and  science  would  be 
impossible.  The  Mathematical  Axioms  would  then  never  be 
applicable  to  Space  or  Time,  nor  to  the  objects  and  processes 
that  fill  them. 

(4)  The  Persistence  of  Matter  and  Energy :  the  physical 
principle  that,  in  all  changes  of  the  universe,  the  quantities 
of  Matter  and  Energy  (actual  and  potential,  so-called)  remain 
the  same. — For  example,  as  to  Matter,  although  dew  is  found 
on  the  grass  at  morning  without  any  apparent  cause,  and 
although  a  candle  seems  to  burn  away  to  a  scrap  of  blackened 
wick,  yet  every  one  knows  that  the  dew  has  been  condensed 
from  vapour  in  the  air,  and  that  the  candle  has  only  turned 
into  gas  and  smoke.  As  to  Energy,  although  a  stone  thrown 
up  to  the  housetop  and  resting  there  has  lost  actual  energy, 
it  has  gained  such  a  position  that  the  slightest  touch  may 
bring  it  to  the  earth  again  in  the  same  time  as  it  took  to 
travel  upwards;  and  in  that  position  it  is  said  to  have 
potential  energy.  When  a  boiler  works  an  engine,  every 
time  the  piston  is  thrust  forward  (having  actual  energy),  an 
equivalent  in  heat  (molecular  energy)  is  lost.  But  for  the 
elucidation  of  these  principles,  readers  must  refer  to  treatises 
of  Chemistry  and  Physics. 

(5)  Causation,  a  special  form  of  the  foregoing  principles 
(4),  we  shall  discuss  in  the  next  chapter. 

(6)  Certain  Uniformities  of  Co-existence ;  but  for  want  of 
a  general  principle  of  Co-existence,  corresponding  to  Causation, 
(the  principles  of  Succession),  we  can  only  classify  these  Uni- 
formities as  follows : 

{a)  The  Geometrical ;  as  that,  in  a  four-sided  figure,  if  the 
opposite  angles  are  equal,  the  opposite  sides  are  equal  and 
parallel.— Countless  similar  Uniformities  of  Co-existence  are 
disclosed  by  Geometry.  The  co-existent  facts  do  not  cause 
one  another,  nor  are  they  jointly  caused  by  something  else ; 
they  are  mutually  involved  :  such  is  the  nature  of  Space. 


144      LOGIC:    DEDUCTIVE    AND    INDUCTIVE 

{b)  Universal  co-existences  among  the  properties  of  concrete 
things. — The  chief  example  is  the  co-existence  of  Gravity  with 
Inertia  in  all  material  bodies.  There  is,  I  believe,  no  other 
entirely  satisfactory  case;  but  some  good  approximations  to 
such  uniformity  are  known  to  phyical  science. 

{c)  Co-existence  due  to  Causation ;  such  as  the  positions  of 
objects  in  space  at  any  time. — The  houses  of  a  town  are  where 
they  are,  because  they  were  put  there;  and  they  remain  in 
their  place  as  long  as  no  other  causes  arise  strong  enough 
to  remove  or  destroy  them.  Similarly,  the  relative  positions 
of  rocks  in  geological  strata,  and  of  trees  in  a  forest,  are  due  to 
causes. 

{d)  The  Co-existence  of  properties  in  Natural  Kinds ;  which 
we  call  the  constitution,  defining  characters,  or  specific  nature 
of  such  things.— Oxygen,  platinum,  sulphur  and  the  other 
elements;  water,  common  salt,  alcohol  and  other  com- 
pounds ;  the  various  species  of  plants  and  animals :  all  these 
are  known  to  us  as  different  groups  of  co-existent  properties. 
It  may  be  conjectured,  indeed,  that  these  groupings  of  proper- 
ties are  also  due  to  causation,  and  sometimes  the  causes  can 
be  traced :  but  very  often  the  causes  are  still  unknown ;  and, 
at  any  rate,  these  cases  of  Co-existence  form  a  sufficiently  Veil- 
marked  class  to  be  separately  mentioned. 

{e)  There  are  also  a  few  cases  in  which  properties  co-exist 
in  an  unaccountable  way,  without  being  co-extensive  with  any 
one  species,  genus,  or  order :  as  most  metals  are  whitish,  and 
scarlet  flowers  are  wanting  in  fragrance. 

So  much,  then,  as  to  the  Uniformity  of  Nature  in  general : 
some  of  its  constituent  principles  have  already  been  discussed ; 
and  Causation  is  such  an  important  one  as  to  require  a 
chapter  to  itself. 

(On  this  §,  see  Venn's  Empirical  Logic,  c.  4.) 


1 
4. 


CHAPTER  XIV 


CAUSATION 


§  I.  For  the  theory  of  Induction,  the  specially  important 
aspect  of  the  Uniformity  of  Nature  is  Causation. 

For  (i)  the  Principles  of  Contradiction  and  Excluded  ^Middle 
are  implied  in  all  logical  operations,  and  need  no  further  expli- 
cation. 

(2)  That  one  thing  is  a  mark  of  another  (except  in  the 
ultimate  modes  of  Uniformity— such  as  the  Law  of  Causation 
Itself— which  are  assumed  in  Logic)  must  be  established  by 
Induction ;  and  the  surest  of  all  marks  is  a  Cause. 

So  that  the  application  of  the  Nota  nohc  in  particular  cases 
requires,  when  most  valid,  a  previous  appeal  to  Causation. 
And  if  we  find  that  the  Nota  7iot(E  is  itself  appealed  to  in 
showing  that  any  given  related  phenomena  are  Cause  and 
Effect,  it  will  only  be  in  the  same  way  as  in  all  Syllogisms,  that 
is  to  say,  as  an  Axiom. 

(3)  The  uniformity  of  Space  and  Time  is,  of  course,  involved 
in  Causation,  if  we  conceive  Causation  as  essentially  matter  in 
motion ;  for  Motion  is  only  known  as  a  traversing  of  Space  in 
Time ;  so  that  if  Space  and  Time  were  not  uniform.  Causation 
would  be  irregular.  But,  though  always  assumed,  this  principle 
need  not  be  explicitly  appealed  to  in  any  particular  investigation; 
since  it  is  only  a  formal  condition ;  for  Time  and  Space  are  not 
agents  or  causes. 

(4)  The  general  persistence  of  Matter  and  Energy,  again, 
although  it  is  nothing  else  than  Causation  in  the  movement  of 
the  world,  is  yet  too  wide  a  principle  to  use  in  esta  Wishing  the 

K 


146      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

cause  of  a  particular  limited  phenomenon,   such  as  a  soap- 
bubble,  or  a  thunder-storm,  or  the  tide. 

(5)  As  to  Co-existences,  the  Geometrical  do  not  belong  to 
Logic  :  those  involved  in  the  existence  of  plants,  animals,  and 
inorganic  bodies,  must,  as  far  as  possible,  be  traced  to  causes ; 
and  so,  of  course,  must  the  relative  positions  of  objects  in  space 
at  any  time :  and  what  Co-existences  remain  do  not  admit  of 
methodical  inductive  treatment ;  they  will  be  briefly  discussed 

in  chap.  xvii. 

We  may  assume,  then,  that  Causation  is  that  mode  or  aspect 
of  the  Uniformity  of  Nature  which  especially  concerns  us  in 
Induction;  and  we  must,  therefore,  make  it  as  definite  as 
possible. 

§  2.  A  Cause,  according  to  Mill,  is  "  the  invariable  uncondi- 
tional antecedent "  of  a  given  phenomenon.  This  definition 
needs  careful  attention. 

(i)  A  Cause  is  relative  to  a  given  phenomenon,  called  the 
Effect.  Logic  has  no  method  for  investigating  the  cause  of 
the  universe  as  a  whole,  but  only  of  a  part  or  epoch  of  it : 
any  portion  that  is  neither  too  large  nor  too  small  for  a  trained 
mind  to  comprehend.  The  magnitude  of  the  phenomenon 
may  be  a  matter  of  convenience.  If  the  cause  of  disease  in 
general  is  too  wide  a  problem,  can  fevers  be  dealt  with ;  or,  if 
that  be  too  much,  is  typhus  within  the  reach  of  inquiry?  In 
short,  how  much  can  we  deal  with  accurately  ? 

(2)  The  given  phenomenon  is  always  an  event:  that  is  to 
say,  not  a  new  thing  (nothing  is  wholly  new),  but  a  change  in 
something  or  in  the  relative  position  of  things.  We  may  ask 
the  cause  of  the  phases  ot  the  Moon,  of  the  freezing  of  water, 
of  a  deposit  of  chalk,  of  the  differentiation  of  species.  To 
inquire  the  cause  of  France  being  a  republic,  or  Russia  an 
autocracy,  imphes  that  these  countries  were  once  otherwise 
governed,  or  had  no  government  :  to  inquire  the  cause  of  the 
earth  being  shaped  like  an  orange,  implies  that  the  matter  of 
the  earth  had  once  another  shape. 

(3)  The  Cause  is  antecedent  to  the  effect,  which  accordingly 


CAUSATION 


147 


t 


is  often  called  its  Consequent.  This  is  often  misunderstood 
and  sometimes  disputed.  It  has  been  said  that  the  meaning 
of  '•  cause '  implies  an  '  effect,'  so  that  until  an  effect  occurs 
there  can  be  no  cause.  But  this  is  a  blunder  \  for  whilst  the 
word  '  cause '  implies  effect,  it  also  implies  the  relative 
futurity  of  the  effect ;  and  effect  implies  the  relative  priority 
of  the  cause.  The  connotation  of  the  words^  therefore,  agrees 
wxU  enough  with  Mill's  doctrine.  In  fact,  the  danger  is  that 
any  pair  of  contrasted  words  may  suggest  too  strongly  that  the 
phenomena  denoted  are  separate  in  nature ;  whereas  every 
natural  process  is  continuous.  If  water,  dripping  from  the 
roof,  wears  away  a  stone,  it  fell  on  the  roof  as  rain ;  the  rain 
came  from  a  condensing  cloud ;  the  cloud  was  driven  by  the 
wind  from  the  sea,  whence  it  exhaled ;  and  so  on.  There  is 
no  beginning  to  this,  and  no  break  in  it.  We  may  take  any 
one  of  these  changes,  call  it  an  effect,  and  ask  for  its  cause ; 
or  call  it  a  cause,  and  ask  for  its  effect.  There  is  not  in 
nature  one  set  of  things  called  causes  and  another  called 
effects ;  but  everything  is  both  cause  of  the  future  and  effect  of 
the  past ;  and  whether  we  consider  an  event  as  the  one  or  the 
other,  depends  upon  the  direction  of  our  curiosity  or  interest. 

Still,  taking  the  event  as  effect,  its  cause  is  the  antecedent 
process ;  or,  taking  it  as  cause,  its  effect  is  the  consequent 
process.  This  follows  from  the  conception  of  causation  as 
essentially  motion ;  for  that  inotion  takes  time  is  (from  the  way 
our  perceptive  powers  grow)  an  ultimate  intuition.  But,  for 
the  same  reason,  there  is  no  interval  of  time  between  cause 
and  effect ;  since  all  the  time  is  filled  up  with  motion. 

Nor  must  it  be  supposed  that  the  whole  cause  is  antecedent 
to  the  effect  as  a  whole :  for  we  often  take  the  phenomenon  on 
such  a  scale  that  minutes,  days,  years,  may  elapse  before  we 
consider  the  cause  as  exhausted  {e.g.,  an  earthquake,  a  battle, 
an  expansion  of  credit) ;  and  all  that  time  the  effect  has  been 
accumulating.  But  we  may  further  consider  such  a  cause  as 
made  up  of  moments  or  minute  factors,  and  the  effect  as  made 
up  of  corresponding  moments ;  and  then  the  cause,  taken  in 


t 


148      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

its  moments,  is  antecedent  throughout  to  the  effect,  taken  in 
its  corresponding  moments. 

(4)  The  Cause  is  the  invariable  antecedent  of  the  effect; 
that  is  to  say,  whenever  a  given  cause  occurs  it  ahvays  has  the 
same  effect :  in  this,  in  fact,  consists  the  Uniformity  of  Causa- 
tion.    Accordingly,  not  every  antecedent  of  an  event  is  its 
Cause  :  to  assume  that  it  is  so,  is  the  familiar  fallacy  of  arguing 
^ post  hoc  ergo  propter  hoc^      But  every  event  has  an  infinite 
number  of  antecedents  that  have  no  ascertainable  connection 
with  it :  if  a  picture  falls  from  the  wall  in  this  room,  there  may 
have  been,  just  before,  an  earthquake  in  New  Zealand,  an 
explosion  in  a  Japanese  arsenal,  a  religious  riot  in  India,  a 
political  assassination  in  Russia  and  a  vote  of  censure  in  the 
House  of  Commons,  besides  millions  of  other  less  noticeable 
events,  between  none  of  which  and  the  falling  of  the  picture 
can  any  direct  causation  be  detected ;  though,  no  doubt,  they 
are  all  necessary  occurrences  in  the  general  world-process,  and 
remotely  connected.     The  Cause,  however,  was  that  a  door 
slammed  violently  in  the  room   above,  and  that   the  picture 
was  heavy  and  the  cord  old  and  rotten.     Even  if  two  events 
invariably  occur  one  after  the  other,  as  day  follows  night,  or 
the  report  follows  the  flash  of  a  gun,  they  may  not  be  Cause 
and  Effect,  though  it  is  highly  probable  that  they  are  closely 
connected  by  Causation ;  and  in  these  two  examples  the  events 
are  of  course  joint  effects  of  a  common  Cause.     Still,  whilst  it 
is  not  true  that  every  antecedent,  or  that  every  invariable  ante- 
cedent, of  an  event  is  its  Cause,  it  is  held  to  be  true  that  the 
Cause  is  something,  or  some  state  and  process  of  things,  such 
that  whenever   it   exactly  recurs    the    same   event   invariably 
follows.     At  the  same  time,  it  must  be  acknowledged  that, 
if  we  consider  the  antecedent   state   and   process   of  things 
very  widely  and  minutely,  it   never   does   exactly  recur.     So 
that   to   construe   the   Law   of  Causation    too   strictly,  is   to 
render  it  inapplicable  not  only  in  practice  but  also  in  scientific 
inquiry.     The  requisite  qualifications  will  appear  in  the  next 
paragraph. 


i 


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CAUSATION 


149 


(5)  The   Cause  is   the   Unconditional   Antecedent. — 'Con- 
dition '  means  any  necessary  factor  of  a  Cause :   a  positive 
Condition  is  one  that  cannot  be  omitted  without  frustrating 
the  effect ;  a  negative  Condition  is  one  that  cannot  be  intro- 
duced without  frustrating  the  effect.     In   the   falling   of  the 
picture,  e.g.^  the  positive  conditions  were  the  slamming  door 
and  the  rottenness  of  the  cord ;  a  negative  condition  was  that 
it  should  have  no  support  but  the  cord.     When  Mill,  then, 
defines  the  Cause  of  any  event  as  its  "unconditional"  ante- 
cedent, he  means  that  it  is  that  group  of  conditions  (state  and 
process  of  things)   which,   without  any  further  condition,   is 
followed  by  the  event  in  question  :  it  is  the  least  antecedent 
that  suffices,  positive  conditions  being  present  and  negative 
absent. 

Now  this  enables  us  to  distinguish  a  true  Cause  from  an 
unconnected  antecedent.  Earthquakes  have  happened  in  New 
Zealand  and  votes  of  censure  in  the  House  of  Commons 
without  a  picture's  falling  in  the  room :  they  were  not  un- 
conditional antecedents ;  something  else  was  needed  to  bring 
down  a  picture.  It  also  distinguishes  a  true  cause  from  an 
invariable  antecedent  that  is  only  a  joint-effect :  for  when  day 
follows  night  something  else  happens ;  the  earth  rotates  upon 
her  axis :  a  flash  even  of  gunpowder  is  not  an  unconditional 
antecedent  of  a  report ;  the  powder  must  be  ignited  in  a  closed 
chamber. 

By  common  experience  and  more  precisely  by  experiment, 
it  is  found  possible  to  select  from  among  the  antecedents  of  an 
event  a  certain  number  upon  which,  so  far  as  can  be  perceived, 
it  is  dependent,  and  to  neglect  the  rest.  Remote  conditions 
may  indeed  modify  the  event  in  ways  so  refined  as  to  escape 
our  notice  :  business  and  science  are  alike  subject  to  the  limi- 
tations of  our  human  faculties.  Subject  to  these  Hmitations, 
however,  we  are  able  in  many  cases  to  secure  an  unconditional 
antecedent  upon  which  a  certain  event  invariably  follows.  In 
ordinary  affairs  everybody  takes  this  for  granted :  if  the  gas 
will  not  burn,  or  a  gun  will  not  go  off,  we  wonder  '  what  can  be 


1 


150      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

wrong  with  it,'  that  is,  what  positive  condition  is  wanting,  or 
what  negative  one  is  present.  And  these  conditions  are  de- 
finitely and  narrowly  conceived.  No  one  now  supposes  that 
gunnery  depends  upon  those  "remotest  of  all  causes,"  the 
stars,  or  upon  the  sun  being  in  Sagittarius  rather  than  in 
Aquarius,  or  that  one  shoots  straightest  with  a  silver  bullet,  or 
after  saying  the  alphabet  backwards. 

(6)  That  the  Cause  of  any  event  is  an  Immediate  Antecedent 
follows  from  its  being  an  Unconditional  one.  For  if  there  are 
three  events,  ABC,  causally  connected,  it  is  plain  that  A  is 
not  the  Unconditional  antecedent  of  C,  but  requires  the 
further  condition  of  first  giving  rise  to  B.  But  that  is  not  all ; 
for  the  B  that  gives  rise  to  C  is  never  merely  the  effect  of  A ; 
it  involves  something  further.  Take  such  a  simple  case  as  the 
motion  of  the  earth  round  the  sun  (neglecting  all  other  con- 
ditions, the  other  planets,  etc^ ;  and  let  the  earth's  motion  at 
three  successive  moments  be  A  B  C  :  A  is  not  the  whole  cause 
of  B  in  velocity  and  direction ;  we  must  add  relation  to  the 
sun,  say  x.  But  then,  again,  the  cause  of  C  will  not  be  merely 
Bx,  for  the  relation  to  the  sun  will  have  altered ;  so  that  we 
must  represent  it  as  Bx'.  The  series,  therefore,  is  Ax  Bx'  C. 
What  is  called  a  "  remote  cause "  is,  therefore,  doubly  con- 
ditional ;  first,  because  it  supposes  an  intervening  cause ;  and, 
secondly,  because  it  only  in  part  determines  the  conditions 
that  constitute  this  intervening  cause. 

But  although  the  Immediacy  of  a  Cause  is  implied  in  its 
Unconditionalness,  it  is  often  so  important  a  clue  to  it  as  to 
deserve  separate  mention.  At  the  same  time,  it  must  be 
acknowledged  that,  as  far  as  the  detection  of  causes  depends 
upon  sense-perception,  our  knowledge  of  Immediacy  is  subject 
to  the  limitations  of  our  perceptive  powers,  which  are  unequal  to 
the  subtlety  of  Nature.  Between  the  event  and  what  seems  to  us 
the  Immediate  Antecedent  many  things  (molecular  changes) 
may  happen  (say)  in  Chemistry.  And  where  phenomena  are 
treated  upon  a  large  scale,  as  in  the  Biological  and  Social 
sciences,  Immediacy,  as  a  mark  of  causation,  must  be  liberally 


CAUSATION 


151 


1 


interpreted.     So  far,  then,  as  to  the  qualitative  character  of 

Causation. 

(7)  But  to  complete  our  account  of  it,  we  must  briefly  con- 
sider its  quantitative  character.  As  to  the  matter  contained, 
and  as  to  the  energy  embodied,  Cause  and  Effect  are  conceived 
to  be  equal.  As  to  Matter,  indeed,  they  may  be  more  properly 
called  identical;  since  the  effect  is  nothing  but  the  cause 
redistributed.  When  oxygen  combines  with  hydrogen  to  form 
water,  or  with  mercury  to  form  red  precipitate,  the  weight 
of  the  compound  is  exactly  equal  to  the  weight  of  the  elements 
combined  in  it ;  when  a  shell  explodes  and  knocks  down  a 
wall,  the  materials  of  the  shell  and  wall  are  scattered  about. 
As  to  Energy,  we  see  that  in  the  heavenly  bodies,  which  meet 
with  no  sensible  impediment,  it  remains  the  same  from  age  to 
age:  with  things  *  below  the  moon'  we  have  to  allow  for 
the  more  or  less  rapid  conversion  of  the  visible  motion  of  a 
mass  into  other  forms  of  energy,  such  as  sound  and  heat. 
But  the  right  understanding  of  this  point  involves  physical 
considerations  of  some  difficulty,  as  to  which  the  reader  must 
refer  to  appropriate  books,  such  as  Balfour  Stewart's  on  The 
Conservation  of  Energy. 

The  comprehension  of  the  quantitative  aspect  of  Causation 
is,  however,  greatly  aided  by  Professor  Bain's  analysis  of  any 
Cause  into  an  Inciting  Power  and  a  Collocation.  When  a 
demagogue  by  making  a  speech  stirs  up  a  mob  to  a  not,  the 
speech  is  the  Inciting  Power ;  the  mo^  already  in  a  state  of 
smouldering  passion,  and  a  street  convenient  to  be  wrecked, 
are  the  Collocation.  When  a  small  quantity  of  strychnine 
kills  a  man,  the  strychnine  is  the  Inciting  Power;  the  nature 
of  his  nervo-muscular  system,  apt  to  be  thrown  into  spasms  by 
that  drug,  and  all  the  organs  of  his  body  dependent  on  that 
system,  are  the  Collocation.  Now  any  one  who  thinks  only  of 
the  speech,  or  the  drug,  in  these  cases,  may  express  astonish- 
ment at  the  disproportion  of  Cause  and  Effect : 

"  What  great  events  from  trivial  causes  spring !  " 

But,  remembering  that  the  whole  cause  of  the  riot  included 


152      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

the  excited  mob,  every  one  sees  that  its  muscular  power  is  enough 
to  wreck  a  street ;  and  remembering  that  breathing  depends 
upon  the  normal  action  of  the  intercostal  muscles,  it  is  plain 
that  if  this  action  is  stopped  a  man  must  die.    Thus,  when  suffi- 
cient energy  to  account  for  any  Effect  cannot  be  found  in  the 
Inciting  Power,  or  manifestly  active  condition,  we  must  look 
for  it  in  the  Collocation  which  is  often  supposed  to  be  passive. 
And  that  reminds  us  of  another  common  misapprehension, 
namely,  that  in   Nature  some  things  are  passive  and  others 
active  :  the  distinction  between  agent  and  patient.     This  is  a 
merely  relative  distinction  :    in  Nature  all  things  are  active. 
To  the  eye  some  things  seem  at  rest  and  others  in  motion  ; 
but  we  know  that  nothing  is  really  at   rest,  that  everything 
palpitates  with  molecular  change,  and  whirls  with  the  planet 
through  space ;  and  the  quietest  looking  object  (say,  a  moss- 
covered  stone),  if  we  try  to  push  or  lift  it,  pushes  or  pulls  us 
back,  assuring  us  that   '  action  and  reaction    are   equal   and 
opposite.'   *  Inertia  '  does  not  mean  want  of  vigour,  but  the  exact 
contrary  ;  and  may  be  metaphorically  described  as  the   inex- 
pugnable resolve  of  everything  to  have  its  own  way.    Such  reflec- 
tions enable  any  one  to  understand  how  cause  and  effect  are 
equal  when  regarded  as  a  transformation  of  Matter  and  Energy. 
This   transformation   of  Matter   and    Energy,  then,   is  the 
essence  of  causation  :  because  it  is  continuous,   causation  is 
immediate ;  and  because  in  the  same  circumstances  the  trans- 
formation always  follows  the  same  course,  a  cause  has  invari- 
ably the  same  effect.     If  a  fire  is  lit  morning  after  morning  in 
the  same  grate,  with  coal,  wood  and  paper  of  the  same  quality 
and   similarly   arranged,   there  will  be   each   time   the   same 
flaming   of  paper,    crackling   of  wood  and  glowing   of  coal, 
followed  in  about  the  same  time  by  the  same  reduction  of  the 
whole  mass  pardy  to  ashes  and  partly  to  gases  that  have  gone 
up   the   chimney.     The   flaming,    crackling  and  glowing   are, 
physically,    so    many   modes  of  energy ;   and   the   change  of 
materials  into  gas  and  ashes  is  a  chemical  and  physical  redis- 
tribution :  and,  if  some  one  is  present,  he  will  be  aware  of  all 


CAUSATION 


153 


v| 


[ 


i 


this ;  and  then,  besides  the  physical  changes,  there  will  be 
sensations  of  light,  sound  and  heat ;  and  these,  again,  will  be 
always  the  same  in  the  same  circumstances. 

The  Cause  of  any  event,  then,  when  exactly  ascertainable, 
has  five  marks  :  it  is  (quantitatively)  equal  to  the  effect,  and  is 
(qualitatively)  its  immediate^  unconditional^i?ivanahIe  antecedent. 
§  3.  This  scientific  conception  of  causation,  however,  has 
been  developed  and  rendered  definite  by  the  investigations  of 
those   physical   sciences   that   can  avail   themselves  of  exact 
experiments  and  mathematical  calculation ;  and  it  is  there,  in 
Chemistry,  Optics,  Thermotics  and  Dynamics,  that  it  is  most 
completely  applicable.     The  conception  can  indeed  be  carried 
into  the  Biological  and  Social  sciences,  even  in  its  quantitative 
form,  by  making  the  proper  allowances.      For  the  limbs  of 
animals  are  levers,  and  act  upon  mechanical  principles  ;  and 
digestion  and   the   aeration    of  the   blood   by   breathing  are 
partly  chemical  processes.     There  is   a   quantitative   relation 
between  the  food  a  man  eats  and  the  amount  of  work  he  can 
do.     The  numbers  of  any  species  of  plant  or  animal  depend 
upon  the  food  supply.     The  value  of  a  country's  imports  is 
equal  to  the  value  of  its  exports  and  of  the  services  it  renders 
to  foreigners.     But,  generally,   the  less  experiment  and  exact 
calculation  are  practicable  in  any  branch  of  inquiry,  the  less 
rigorously  can  the  conception  of  Causation  be  applied  there ; 
the  more,  too,  will  its  application  depend  upon  the  quaUtative 
marks,  and  the  more  need  there  will  be  to  use  it  judiciously. 
It  is  unreasonable  to  expect  in  any  case  more  precise  proofs 
than  the  subject  admits  of. 

Wherever  mental  action  is  involved,  there  is  a  special 
difficulty  in  applying  the  physical  notion  of  Causation.  For, 
clearly,  if  a  Cause  is  conceived  as  matter  in  motion,  a  thought, 
*  or  feeling,  or  volition  can  be  neither  Cause  nor  Effect.  And 
since  mental  action  is  involved  in  all  social  affciirs,  and  in  the 
life  of  all  men  and  animals,  it  may  seem  impossible  to 
interpret  social  or  vital  changes  according  to  laws  of  Causa- 
tion.     Still,  animals  and  men  are   moving  bodies;  and  it  is 


ii 


154      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

recognised  that  their  thoughts  and  feelings  are  connected  with 
their  movements  and  with  the  movements  of  other  things  that 
act  upon  them,  so  that  we  can  judge  of  one  case  by  another ; 
although  the  connection  is  by  no  means  well  understood,  and 
the  best  words  (such  as  all  can  agree  to  use)  have  not  yet  been 
found  to  express  even  what  we  know  about  it.  Hence,  a 
regular  connection  being  granted,  I  have  not  hesitated  to  use 
biological  and  social  events  and  the  laws  of  them,  to  illustrate 
causation  and  Induction  ;  because,  though  less  exact  than 
chemical  or  mechanical  examples,  they  are  to  most  people 
more  familiar  and  interesting. 

In  practical  affairs,  it  is  felt  that  everything  depends  upon 
Causation  :  how  to  play  the  fiddle,  or  sail  a  yacht,  or  get  one's 
living,  or  defeat  the  enemy.  The  price  of  pig-iron  six  months 
hence,  the  prospects  of  the  harvest,  the  issue  in  a  Coroner's 
court.  Home  Rule  and  Socialism,  are  all  questions  of  causation. 
But,  in  such  cases,  the  conception  of  a  Cause  is  rarely  applied 
in  its  full  scientific  acceptation,  as  the  unconditional  ante- 
cedent, or  '  all  the  conditions '  (neither  more  nor  less)  upon 
which  the  event  depends.  This  is  not  because  men  of  business 
are  bad  logicians,  or  incapable  of  scientific  comprehension ; 
for  very  often  the  reverse  is  conspicuously  true ;  but  because 
practical  affairs  call  for  promptitude  and  a  decisive  seizing  upon 
what  is  predominantly  important.  How  learn  to  play  the  fiddle  ? 
*'  Go  to  a  good  teacher."  (Then,  beginning  young  enough, 
with  natural  aptitude  and  great  diligence,  all  may  be  well.) 
How  defeat  the  enemy  ?  "  Be  two  to  one  at  the  critical 
juncture."  (Then,  if  the  men  are  brave,  disciplined,  well 
armed  and  well  fed,  there  is  a  good  chance  of  victory.)  Will 
the  price  of  iron  improve  ?  '*  Yes  :  for  the  market  is  over- 
sold ":  (that  is,  many  have  sold  iron  who  have  none  to  deliver, 
and  must  at  some  time  buy  it  back ;  and  that  will  put  up  the 
price — if  the  stock  is  not  too  great,  if  the  demand  does  not 
fall  off,  and  if  those  who  have  bought  what  they  cannot  pay  for 
are  not  in  the  meanwhile  obliged  to  sell.)  These  prompt  and 
decisive  judgments  as  to  what  is  the  Cause,  or  predominantly 


CAUSATION 


155 


V, 


important  condition,  of  any  event,  are  not  as  good  as  a  scientific 
estimate  of  all  the  conditions,  when  this  can  be  obtained  ;  but, 
when  time  is  short,  the  insight  of  trained  sagacity  may  be  much 
better  than  an  imperfect  theoretical  treatment  of  such  problems. 

§  4.  To  regard  the  Effect  of  certain  antecedents  in  a  narrow 
selective  way,  is  another  common  mistake.  In  the  full  scientific 
conception  of  an  Effect,  it  is  the  sum  of  the  unconditional 
consequences  of  a  given  state  and  process  of  things  :  the 
consequences  immediately  flowing  from  that  situation  without 
further  conditions.  Always  to  take  account  of  all  the  con- 
sequences of  any  Cause  would  no  doubt  be  impracticable ;  still 
the  practical,  as  well  as  the  scientific  interest,  often  requires 
that  we  should  enlarge  our  views  of  them.  An  important 
consequence  of  eating  is  to  satisfy  hunger,  and  this  is  the 
ordinary  motive  to  eat ;  but  it  is  a  poor  account  of  the  effect, 
including  its  physiological  consequences.  All  sorts  of  food 
'  satisfy  hunger ' ;  but  for  health  and  strength  some  sorts  are 
much  better  than  others.  An  important  consequence  of  firing 
a  gun  is  the  propulsion  of  the  bullet  or  shell ;  but  there  are 
many  other  consequences  in  the  whole  effect,  and  one  of 
them  is  the  heating  of  the  gun,  which,  accumulating  with  rapid 
firing,  may  at  last  put  the  gun  out  of  action.  The  tides  have 
consequences  to  shipping  and  in  the  wear  and  tear  of  the  coast 
that  draw  every  one's  attention ;  but  we  are  told  that  they  also 
retard  the  rotation  of  the  earth,  and  at  last  may  cause  it  to 
present  always  the  same  face  to  the  sun  and,  therefore,  to  be 
uninhabitable.  Such  concurrent  consequences  of  any  Cause 
may  be  called  its  co-effects  :  the  Effect  being  the  sum  of  them. 

The  neglect  to  take  account  of  the  whole  Effect  (that  is, 
of  all  the  co-effects)  in  any  case  of  causation,  is  perhaps  the 
reason  why  many  philosophers  have  maintained  the  doctrine 
of  a  "  Plurality  of  Causes  "  :  meaning  not  that  more  than  one 
condition  is  operative  in  the  antecedent  of  every  event  (which 
is  true),  but  that  the  same  event  may  be  due  at  different  times 
to  different  antecedents,  that  in  fact  there  may  be  vicarious 
Causes.     If,  however,  we  take  any  Effect  as  a  whole,  this  does 


156      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

not  seem  to  be  true.  A  fire  may  certainly  be  lit  in  many  ways  : 
with  a  match  or  a  flint  and  steel,  or  by  rubbing  sticks  together, 
or  by  a  flash  of  lightning  :  have  we  not  here  a  plurality  of 
causes  ?  Not  if  we  take  account  of  the  whole  Effect ;  for  then 
we  shall  find  it  modified  in  each  case  according  to  the 
difference  of  the  Cause.  In  one  case  there  will  be  a  burnt 
match,  in  another  a  warm  flint,  in  the  last  a  changed  state  of 
electrical  tension.  And  similar  differences  would  be  found  in 
cases  of  death  under  different  conditions,  as  stabbing,  hanging, 
cholera  ;  or  of  shipwreck  from  explosion,  scuttling,  tempest. 
In  short,  if  we  knew  the  facts  minutely  enough,  it  would  be 
found  that  there  is  only  one  Cause  (sum  of  conditions)  for  each 
Effect  (sum  of  co-effects),  and  that  the  order  of  events  is  as 
uniform  backwards  as  forwards. 

Still,  as  we  are  far  from  knowing  events  minutely,  it  is 
necessary  in  practical  affairs  and  even  in  the  more  complex  and 
unmanageable  scientific  investigations,  especially  those  that  deal 
with  human  life,  to  acknowledge  a  possible  Plurality  of  Causes 
for  any  effect.  Indeed,  forgetfulness  of  this  leads  to  many  rash 
generalisations  ;  as  that  '  revolutions  always  begin  in  hunger ' ; 
or  that  '  myths  are  a  disease  of  language.'  Then  there  is  great 
waste  of  ingenuity  in  reconciling  such  propositions  with  the 
recalcitrant  facts.  A  scientific  method  recognises  that  there 
may  be  other  causes  of  effects  thus  vaguely  conceived,  and 
then  proceeds  to  distinguish  in  each  class  of  effects  the 
peculiarities  due  to  different  causes. 

§  5.  The  understanding  of  the  complex  nature  of  Causes 
and  Effects  helps  us  to  overcome  some  other  difficulties  that 
perplex  the  use  of  these  words.  We  have  seen  that  the  true 
cause  is  an  immediate  antecedent ;  but  if  the  cause  is  con- 
founded with  one  of  its  constituent  conditions,  it  may  seem  to 
have  long  preceded  the  event  which  is  regarded  as  its  effect. 
Thus,  if  one  man's  death  is  ascribed  to  another's  desire  of 
revenge,  this  desire  may  have  been  entertained  for  years  before 
the  assassination  occurred  :  similarly,  if  a  shipwreck  is  ascribed 
to  a  sunken  rock,  the  rock  was  waiting  for  ages  before  the  ship 


CAUSATION 


157 


f 

^ 


i 


sailed  that  way.  But,  of  course,  neither  the  desire  of  revenge 
nor  the  sunken  rock  was  '  the  sum  of  the  conditions  '  on  which 
the  one  or  the  other  event  depended. 

We  have  also  seen  that  the  true  effect  of  any  state  or  process 
of  things  is  the  immediate  consequence  ;  but  if  the  effect  is 
confounded  with  one  of  its  constituent  factors,  it  may  seem  to 
long  outlive  the  cessation  of  the  cause.     Thus,  in  nearly  every 
process  of  human  industry  and  art,  one  factor  of  the  effect— a 
road,  a  house,  a  tool,  a  picture— may,  and   generally  does, 
remain  long  after  the  work  has  ceased :  but  such  a  result  is 
not  the  whole  effect  of  the  operations  that  produce  it.     The 
other  factors  may  be,  and  some  always  are,  evanescent.     In 
most  of  such  works  some  heat  is  produced  by  hammering  or 
friction,  and  the  labourers  are  fatigued ;  but  these  consequences 
soon  pass  off.     Hence  the  Effect  as  a  whole  only  momentarily 
survives  the  Cause.     Consider  a  pendulum  which,  having  been 
once  set  agoing,  swings  to  and  fro  in  an  arc,  under  the  joint 
control  of  the  shaft,  gravitation  and  its  own  inertia  :  at  every 
moment  its  speed  and  direction  change  ;  and  each  change  may 
be  considered  as  an  effect,  of  which  the  antecedent  change  was 
one  condition.     In  such  a  case  as  this,  which,  though  a  very 
simple,  is  a  perfectly  fair  example  of  all  causation,  the  duration 
of  either  Cause  or  Effect  is  quite  insensible  :  so  that,  as  Dr. 
Venn  says,  an  Effect,  rigorously  conceived,  is  only  "the  initial 
tendency  "  of  its  Cause. 

§  6.  Mill  contrasted  two  forms  under  which  causation  appears 
to  us :  that  is  to  say,  the  conditions  constituting  a  cause  may 
be  modified  or  '  intermixed '  in  the  effect  in  two  ways,  which 
are  typified  respectively  by  Mechanical  and  Chemical  action. 
In  Mechanical  causation,  which  is  found  in  Astronomy  and  all 
branches  of  Physics,  the  effects  are  all  reducible  to  modes  of 
Energy,  and  are  therefore  commensurable  with  their  causes. 
They  are  either  directly  commensurable,  as  in  the  cases  treated 
of  in  the  consideration  of  the  mechanical  powers;  or,  if 
different  forms  of  energy  enter  into  cause  and  effect,  such  as 
mechanical  energy,  electrical  energy,  heat,  these  different  forms 


158      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

are  severally  reducible  to  units,  between  which  equivalents  have 
been  established.  Hence  Mill  calls  this  the  ''homogeneous 
intermixture  of  effects,"  because  the  antecedents  and  conse- 
quents are  fundamentally  of  the  same  kind. 

In  Chemical  causation,  on  the  other  hand,  cause  and  effect 
(at  least  as  they  present  themselves  to  us)  differ  in  almost 
every  way  :  in  the  act  of  combination  the  properties  of  the 
elements  disappear,  and  are  superseded  by  others  in  the  com- 
pound. If,  for  example,  mercury  (a  heavy,  silvery  liquid)  be 
heated  in  contact  with  oxygen  (a  colourless  gas),  oxide  of 
mercury  is  formed  (red  precipitate,  which  is  a  powder).  The 
compound  presents  very  different  phenomena  from  those  of  the 
elements ;  and  hence  Mill  called  this  class  of  cases  "  the  hetero- 
pathic  intermixture  of  effects."  Still,  in  chemical  action,  the 
effect  is  not  (in  Nature)  heterogeneous  with  the  cause :  for  the 
weight  of  a  compound  is  equal  to  the  sum  of  the  weights  of  the 
elements  that  are  merged  in  it ;  and  an  equivalence  has  been 
ascertained  between  the  energy  of  chemical  combination  and 
the  heat,  light,  etc.y  produced  in  the  act  of  combination. 

The  heteropathic  intermixture  of  effects  is  also  found  in 
organic  processes  (which,  indeed,  are  partly  chemical) :  as 
when  a  man  eats  bread  and  milk,  and  by  digestion  and 
assimilation  converts  them  into  nerve,  muscle  and  bone. 
Such  phenomena  may  make  us  wonder  that  people  should 
ever  have  believed  that  '  effects  resemble  their  causes.'  A 
dim  recognition  of  the  equivalence  of  cause  and  effect  in 
respect  of  matttr  and  motion,  may  have  aided  the  belief;  and 
the  resemblance  of  offspring  to  parents  may  have  helped  ;  but  it 
has  been  thought  to  be  chiefly  a  confusing  of  the  order  of  images 
in  the  mind  with  the  order  of  events  m  nature.  After  enough 
experience,  the  thought  of  any  event  makes  us  anticipate  its 
consequences,  or  form  a  picture  of  them  before  they  happen  ; 
but  again,  any  image  in  the  mind  often  reminds  us  of  something 
similar,  and  this  may  be  mistaken  for  the  anticipation  of  an 
effect.  Hence,  whistling  is  seriously  regarded  as  a  means  of 
raising  the  wind,  because  the  wind  whistles ;   and  barbarous 


CAUSATION 


159 


rain-makers  sometimes  torment  a  child  to  tears  that  the  clouds 
also  may  weep.     (See  Tylor's  Primitive  Culture,  ch.  4.) 

§7.  There  is  another  consideration  arising  out  of  the  complex 

character  of  causes  and  effects.  When  a  cause  consists  of 
two  or  more  conditions  or  forces,  we  may  consider  what  effect 
any  one  of  them  would  have  if  it  operated  alone,  that  is  to  say,  its 
Tendency.  This,  now,  is  best  illustrated  by  the  Parallelogram 
of  Forces :  if  two  forces  acting  upon  a  point,  but  not  in  the 
same  direction,  be  represented  by  straight  lines  drawn  in  the 
direction  of  the  forces,  and  in  length  proportional  to  their 
magnitudes,  these  lines,  meeting  in  an  angle,  represent  severally 
the  Tendencies  of  the  forces ;  whilst  if  the  parallelogram  be 
completed  on  these  lines,  the  diagonal  drawn  from  the  point  in 
which  they  meet  represents  their  Resultant  or  effect. 

Again,  considering  the  Tendency  of  any  force  if  it  operated 
alone,  we  may  say  that,  when  combined  with  another  force 
(not  in  the  same  direction)  in  any  Resultant,  its  Tendency  is 
counteracted  either  partially  or  wholly.  If  the  other  force  be 
equal  and  opposite,  the  Resultant  is  equilibrium ;  if  it  be  in 
the  same  direction,  the  two  are  merely  added  together. 
Counteraction  is  only  one  mode  of  combination. 

Sometimes  the  separate  Tendencies  of  combined  forces  can 
only  be  theoretically  distinguished :  as  when  the  motion  of  a 
projectile  is  analysed  into  a  Tendency  to  travel  in  the  straight 
line  of  its  discharge,  and  a  Tendency  to  fall  straight  to  the 
ground.     But  sometimes  a  Tendency  can  be  isolated  :  as  when, 
—after  dropping  a  feather  in  some  place  sheltered  from  the 
wind,  and  watching  it  drift  to  and  fro,  as  the  air,  offering 
unequal  resistances  to  its  uneven  surface,  counteracts  its  weight 
with  varying  success,  until  it  slowly  settles  upon  the  ground, — 
we  take  it  up  and  drop  it  again  in  a  vacuum,  when  it  falls  like 
lead.     Here  we  have  the  Tendency  of  a  certain  Cause  (namely, 
the   relation   between   the   feather  and  the  earth)  free  from 
Counteraction  :  and  this  is  called  the  elimination  of  the  counter- 
acting circumstances.     In  this  case  indeed  there  is  physical 
elimination ;  whereas,  in  the  case  of  a  projectile,  when  we  say 


158      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

are  severally  reducible  to  units,  between  which  equivalents  have 
been  established.  Hence  Mill  calls  this  the  "homogeneous 
intermixture  of  effects,"  because  the  antecedents  and  conse- 
quents are  fundamentally  of  the  same  kind. 

In  Chemical  causation,  on  the  other  hand,  cause  and  effect 
(at  least  as  they  present  themselves  to    us)  differ  in  almost 
every  way  :   in  the  act  of  combination  the  properties  of  the 
elements  disappear,  and  are  superseded  by  others  in  the  com- 
pound.    If,  for  example,  mercury  (a  heavy,  silvery  liquid)  be 
heated  in  contact  with  oxygen   (a  colourless  gas),   oxide  of 
mercury  is  formed  (red  precipitate,  which  is  a  powder).     The 
compound  presents  very  different  phenomena  from  those  of  the 
elements ;  and  hence  Mill  called  this  class  of  cases  "  the  hetero- 
pathic  intermixture  of  effects."     Still,  in  chemical  action,  the 
effect  is  not  (in  Nature)  heterogeneous  with  the  cause :  for  the 
weight  of  a  compound  is  equal  to  the  sum  of  the  weights  of  the 
elements  that  are  merged  in  it ;  and  an  equivalence  has  been 
ascertained  between  the  energy  of  chemical  combination  and 
the  heat,  light,  e/c,  produced  in  the  act  of  combination. 

The  heteropathic  intermixture  of  effects  is  also  found  in 
organic  processes  (which,  indeed,  are  partly  chemical):  as 
when  a  man  eats  bread  and  milk,  and  by  digestion  and 
assimilation  converts  them  into  nerve,  muscle  and  bone. 
Such  phenomena  may  make  us  wonder  that  people  should 
ever  have  believed  that  *  effects  resemble  their  causes.'  A 
dim  recognition  of  the  equivalence  of  cause  and  effect  in 
respect  of  matter  and  motion,  may  have  aided  the  belief;  and 
the  resemblance  of  offspring  to  parents  may  have  helped  ;  but  it 
has  been  thought  to  be  chiefly  a  confusing  of  the  order  of  images 
in  the  mind  with  the  order  of  events  in  nature.  After  enough 
experience,  the  thought  of  any  event  makes  us  anticipate  its 
consequences,  or  form  a  picture  of  them  before  they  happen  ; 
but  again,  any  image  in  the  mind  often  reminds  us  of  something 
similar,  and  this  may  be  mistaken  for  the  anticipation  of  an 
effect.  Hence,  whistling  is  seriously  regarde"a  as  a  means  of 
raising  the  wind,  because  the  wind  whistles ;   and  barbarous 


CAUSATION 


159 


^1 


il 


1 


rain-makers  sometimes  torment  a  child  to  tears  that  the  clouds 
also  may  weep.     (See  Tylor's  Primitive  Culture^  ch.  4.) 

§  7.  There  is  another  consideration  arising  out  of  the  complex 
character  of  causes  and  effects.  When  a  cause  consists  of 
two  or  more  conditions  or  forces,  we  may  consider  what  effect 
any  one  of  them  w^ould  have  if  it  operated  alone,  that  is  to  say,  its 
Tendency.  This,  now,  is  best  illustrated  by  the  Parallelogram 
of  Forces:  if  two  forces  acting  upon  a  point,  but  not  in  the 
same  direction,  be  represented  by  straight  Hnes  drawn  in  the 
direction  of  the  forces,  and  in  length  proportional  to  their 
magnitudes,  these  lines,  meeting  in  an  angle,  represent  severally 
the  Tendencies  of  the  forces;  whilst  if  the  parallelogram  be 
completed  on  these  lines,  the  diagonal  drawn  from  the  point  in 
which  they  meet  represents  their  Resultant  or  effect. 

Again,  considering  the  Tendency  of  any  force  if  it  operated 
alone,  we  may  say  that,  when  combined  with  another  force 
(not  in  the  same  direction)  in  any  Resultant,  its  Tendency  is 
counteracted  either  partially  or  wholly.  If  the  other  force  be 
equal  and  opposite,  the  Resultant  is  equihbrium ;  if  it  be  in 
the  same  direction,  the  two  are  merely  added  together. 
Counteraction  is  only  one  mode  of  combination. 

Sometimes  the  separate  Tendencies  of  combined  forces  can 
only  be  theoretically  distinguished ;  as  when  the  motion  of  a 
projectile  is  analysed  into  a  Tendency  to  travel  in  the  straight 
line  of  its  discharge,  and  a  Tendency  to  fall  straight  to  the 
ground.  But  sometimes  a  Tendency  can  be  isolated  :  as  when, 
— after  dropping  a  feather  in  some  place  sheltered  from  the 
wind,  and  watching  it  drift  to  and  fro,  as  the  air,  offering 
unequal  resistances  to  its  uneven  surface,  counteracts  its  weight 
with  varying  success,  until  it  slow^ly  settles  upon  the  ground, — 
we  take  it  up  and  drop  it  again  in  a  vacuum,  when  it  falls  like 
lead.  Here  we  have  the  Tendency  of  a  certain  Cause  (namely, 
the  relation  between  the  feather  and  the  earth)  free  from 
Counteraction  :  and  this  is  called  the  elimination  of  the  counter- 
acting circumstances.  In  this  case  indeed  there  is  physical 
elimination ;  whereas,  in  the  case  of  a  projectile,  when  we  say 


i6o      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


that  its  actual  motion  is  resolvable  (neglecting  the  resistance  of 
the  air)  into  two  Tendencies,  one  in  the  line  of  discharge,  the 
other  earthwards,  there  is  only  theoretical  elimination  of  either 
Tendency,  considered  as  counteracting  the  other ;  and  this  is 
more  specifically  called  the  Resolution  or  Analysis  of  the  total 
effect  into  its  component  conditions.  Now  Elimination  and 
Resolution  may  be  said  to  be  the  essential  process  of  Induction 
in  the  widest  sense  of  the  term,  as  including  the  combination 
of  Induction  with  Deduction. 

The  several  conditions  constituting  any  cause,  then,  by 
aiding  or  counteracting  one  another's  tendencies,  jointly 
determine  the  total  effect.  Hence,  viewed  in  relation  one  to 
another,  they  may  be  said  to  stand  in  Reciprocity  or  mutual 
influence.  This  relation  is  itself  one  of  co-existence,  though  it 
is  conceived  with  reference  to  a  possible  effect.  As  Kant  says, 
all  substances,  as  perceived  in  space  at  the  same  time,  are  in 
reciprocal  activity.  And  what  is  true  of  the  world  of  things  at 
any  moment  (as  connected,  say,  by  gravity)  is  true  of  any 
selected  group  of  circumstances  which  we  regard  as  the 
particular  cause  of  any  event  to  come.  But  we  must  not  think 
of  Reciprocity  as  obtaining  in  the  succession  of  cause  and 
effect,  as  if  the  effect  could  turn  back  upon  its  cause ;  for  as  the 
effect  arises  its  cause  disappears,  and  is  irrecoverable  by  Nature 
or  Magic. 


J 


r 


CHAPTER  XV 


INDUCTIVE   METHOD 


§  I.  It  is  necessary  to  describe  briefly  the  process  of  investi- 
gaiing  laws  of  causation,  not  with  the  notion  of  teaching 
any  one  the  Art  of  Discovery,  which  each  man  pursues  for 
himself  according  to  his  natural  gifts  and  his  experience  in 
the  methods  of  his  own  science,  but  merely  to  cast  some  light 
upon  the  contents  of  the  next  few  chapters.  Logic  is  here 
treated  as  a  process  of  proof;  proof  supposes  that  some  general 
proposition  has  been  suggested  as  requiring  proof;  and  the 
search  for  such  propositions  springs  from  scientific  curiosity. 

We  may,  as  Professor  Bain  observes,  desire  to  detect  a 
process  of  causation  either,  first,  amidst  circumstances  that 
have  no  influence  upon  the  process  but  only  obscure  it; 
as  when,  being  pleased  with  a  certain  scent  in  a  garden, 
we  wish  to  know  from  what  flower  it  rises ;  or,  being  attracted 
by  the  sound  of  some  instrument  in  an  orchestra,  we  desire  to 
know  which  it  is  :  or,  secondly,  amidst  circumstances  that  alter 
the  effect  from  what  it  would  have  been  by  the  sole  operation 
of  some  Cause ;  as  when  the  air  deflects  a  falling  feather ;  or  in 
some  more  complex  case,  such  as  the  problem  now  (1895) 
exciting  so  much  interest,  the  fall  of  prices  that  has  gone  on 
during  the  last  twenty  years.     To  what,  men  ask,  is  this  due  ? 

The  first  step  of  Elimination  (as  Professor  Bain  further 
observes)  is  "to  analyse  the  situation  mentally,"  in  the  light 
of  analogies  suggested  by  our  experience  or  previous  know- 
ledge. Dew,  for  example,  is  moisture  formed  upon  the  surface 
of  bodies  from  no  apparent  source.     But  two  possible  sources 

L 


J.\ 


i62      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


are  easily  suggested  by  common  experience :  is  it  deposited 
from  the  air,  like  the  moisture  upon  a  mirror  when  we  breathe 
upon  it;  or  does  it  exude  from  the  bodies  themselves,  like 
gum  or  turpentine  ?  Or,  again,  as  to  the  fall  of  prices,  a  little 
experience  in  business,  or  knowledge  of  Economics,  readily 
suggests  two  possible  explanations  :  either  cheaper  production 
in  making  goods  or  in  carrying  them  ;  or  a  scarcity  of  that  in 
which  the  purchasing  power  of  the  chief  commercial  nations  is 
directly  expressed,  namely,  gold.     (Bain's  Logic:  B.  III.  c.  v.) 

Having  thus  analysed  the  situation  and  considered  the 
possibility  of  one,  two,  three,  or  more  possible  Causes,  we  fix 
upon  one  of  them  for  further  investigation  ;  that  is  to  say,  we 
frame  an  Hypothesis  that  this  is  the  Cause.  When  an  Effect 
is  given  to  find  its  Cause,  an  inquirer  nearly  always  begins  his 
investigations  by  thus  framing  an  Hypothesis  as  to  the  Cause. 

The  next  step  is  to  try  to  verify  this  Hypothesis.  This 
we  may  sometimes  do  by  varying  the  circumstances  of  the 
phenomenon,  according  to  the  Canons  of  Inductive  Proof 
to  be  discussed  in  the  next  chapter ;  that  is  to  say,  by  observing 
or  experimettting  in  such  a  way  as  to  get  rid  of  or  eliminate 
the  obscuring  or  disturbing  conditions.  Thus,  to  find  out 
which  flower  in  a  garden  gives  a  certain  scent,  it  is  usually 
enough  to  rely  on  observation,  going  up  to  the  likely  flowers 
one  after  the  other  and  smelling  them :  at  close  quarters,  the 
greater  relative  intensity  of  the  smell  is  sufficiently  decisive. 
Or  we  may  resort  to  a  sort  of  experiment,  plucking  a  likely 
flower,  as  to  which  we  frame  the  Hypothesis  (this  is  the  Cause) 
and  carrying  it  to  some  place  where  the  air  is  free  from  con- 
flicting odours. 

But  if  the  phenomenon  is  so  complex  and  extensive  as 
the  recent  fall  of  prices,  direct  observation  or  experiment  is 
a  useless  or  impossible  method ;  and  we  must  then  resort 
to  Deduction.  If,  for  example,  we  take  the  Hypothesis  that 
the  fall  is  due  to  a  scarcity  of  gold,  we  must  show  that  there 
is  a  scarcity ;  what  effect  such  a  scarcity  may  be  expected  to 
have  upon  prices  from  the  'acknowledged  laws  of  prices,  and 


INDUCTIVE    METHOD 


163 


from  the  analogy  of  other  cases  of  an  expanded  or  restricted 
currency;  that  this  expectation  agrees  with  the  statistics  of 
recent  commerce ;  and  finally  that  the  alternative  Hypothesis 
that  the  fall  is  due  to  cheaper  production  is  not  true ;  either 
because  there  has  not  been  a  sufficient  cheapening  of  general 
production  ;  or  because,  if  there  has  been,  the  results  to  be 
rationally  expected  from  it  are  not  such  as  to  agree  with  the^ 
statistics  of  recent  commerce.     (Ch.  xviii.  ) 

But  now  suppose  that,  a  phenomer^on  having  been  suggested 
for  explanation,  we  are  unable  at  the  time  to  think  of  any 
Cause— to  frame  any  Hypothesis  about  it ;  we  must  then  wait 
for  the  phenomenon  to  occur  again  and,  once  more  observing 
its  course  and  accompaniments  and  trying  to  recall  its  ante- 
cedents, do  our  best  to  frame  an  Hypothesis  about  it,  and 
proceed  as  before.  Thus,  in  the  recent  epidemic  of  influenza, 
some  doctors  framed  the  Hypothesis  that  it  was  due  to  a 
deluge  in  China,  others  to  a  volcanic  eruption  near  Java  ;  some 
thought  it  a  mild  form  of  Asiatic  plague,  and  others  caught  a 
specific  microbe.  As  the  disease  often  recurred,  there  were 
fresh  opportunities  of  framing  Hypotheses.  I  do  not  know 
whether  any  one  of  them  has  been  established.  If  not,  we 
must  wait  for  the  next  epidemic. 

Again,  however,  the  investigation  may  take  a  different  form  : 
given  a  supposed  Cause  to  find  its  Effect ;  e.g.,  a  new  chemical 
element,  to  find  what  compounds  it  forms  with  other  elements ; 
or,  the  spots  on  the  sun,  have  they  any  influence  upon  our 
weather  ? 

Here,  then,  if  the  Cause  is  under  control,  as  a  new  element 
may  be,  it  is  possible  to  try  experiments  with  it  according  to 
the  Canons  of  Inductive  Proof.  The  inquirer  may  form  some 
hypothesis  or  expectation  as  to  the  effects,  to  guide  his  obser- 
vation of  them,  but  will  be  careful  not  to  hold  his  expectation  so 
confidently  as  to  falsify  his  observation  of  what  actually  happens. 

But  if  the  Cause  is,  like  the  sun-spots,  not  under  control, 
the  inquirer  will  watch  on  all  sides  what  events  follow  their 
appearance  and  development :  he  must  watch  for  consequences 


164      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

of  the  new  cause  he  is  studying  in  many  different  circumstances, 
that  his  observations  may  satisfy  the  canons  of  Proof.  But  he 
will  also  resort  for  guidance  to  Deduction ;  arguing  from  the 
nature  of  the  Cause,  if  anything  is  known  of  its  nature,  what 
consequences  may  be  expected,  and  comparing  the  results  of 
this  deduction  with  any  consequent  which  he  suspects  to  be 
connected  with  the  cause;  and  of  course,  if  the  results  of 
Deduction  and  Observation  agree,  ho  will  still  consider  whether 
the  facts  observed  may  not  be  due  to  some  other  cause. 

A  Cause,  however,  may  be  under  control  and  yet  be  too 
dangerous  to  experiment  with ;  such  as  a  proposed  change  of 
the  constitution  by  legislation  ;  or  even  some  minor  Act  of 
Parliament,  for  altering  the  Poor  Law,  or  regulating  the  hours 
of  labour.  Here  the  first  step  must  be  Deductive.  We  must 
ask  what  consequences  are  to  be  expected  from  the  nature  of 
the  change  (comparing  it  with  similar  changes),  and  from  the 
laws  of  the  special  circumstances  in  which  it  is  to  operate? 
And  sometimes  we  may  partially  verify  our  deduction  by  try- 
ing experiments  upon  a  small  scale  or  in  a  mild  form.  There 
are  conflicting  deductions  as  to  the  probable  efi'ect  of  giving 
Home  Rule  to  Ireland  ;  and  experiments  have  been  made  in 
more  or  less  similar  cases,  as  in  the  Colonies  and  in  some 
foreign  countries.  It  has  also  been  proposed  to  make  eight 
hours  the  legal  limit  of  a  day's  labour  in  all  trades.  We  have 
all  tried  to  forecast  the  consequences  of  this ;  and  by  way  of 
verification  we  might  begin  with  nine  hours;  or  we  might 
induce  some  other  country  to  try  the  experiment  first.  Still, 
no  verification  by  experiments  on  a  small  scale,  or  in  a  mild 
form,  or  in  somewhat  similar  yet  very  different  circumstances, 
can  be  considered  logically  conclusive.  What  proofs  are  con- 
clusive we  shall  see  in  the  following  chapters. 

§  2.'  To  begin  with  the  conditions  of  direct  Induction. — An 
Induction  is  an  universal  real  proposition,  based  on  observa- 
tion, in  reliance  on  the  uniformity  of  nature  :  when  well  ascer- 
tained, it  is  called  a  Law.  Thus,  that  all  life  depends  on  the 
presence  of  oxygen  is  (i)  an  universal  proposition;  (2)  a  real 


r. 


INDUCTIVE   METHOD 


165 


one,  since  the  'presence  of  oxygen'  is  not  connoted  by  'life'; 
(3)  it  is  based  on  observation  ;  (4)  it  relies  on  the  uniformity 
of  nature,  since  all  cases  of  life  have  not  been  examined. 

It  should  be  observed  that  such  a  proposition  is  here  called 
an  Induction,  when  it  is  inductively  proved ;  that  is,  proved 
by  facts,  not  deduced  from  more  general  premises  (except  the 
premise  of  nature's  uniformity) :  and  by  the  '  process  of  Induc- 
tion' is  meant  the  method  of  inductive  proof.  The  phrase 
*  process  of  Induction  '  is  often  used  in  another  sense,  namely, 
for  the  inference  or  judgment  by  which  such  propositions  are 
arrived  at.  But  it  is  better  to  call  this  the  process  of  hypothe- 
sis, and  to  regard  it  as  a  preliminary  to  the  process  of  Induc- 
tion (that  is,  proof),  as  furnishing  the  hypothesis  which,  if  it 
can  stand  the  proper  tests,  becomes  an  Induction  or  Law. 

§  3.  Inductive  proofs  are  usually  classed  as  Perfect  and  Im- 
perfect. They  are  said  to  be  Perfect  when  all  the  instances 
within  the  scope  of  the  given  proposition  have  been  severally 
examined,  and  the  proposition  has  been  found  true  in  each 
case.  But  we  have  seen  (chap.  xii.  §  i)  that  the  instances 
included  in  universal  propositions  concerning  Causes  and  Kinds 
cannot  be  exhaustively  examined  :  we  do  not  know  all  planets, 
all  heat,  all  liquids,  all  life,  eU. ;  and  we  never  can,  since  a 
man's  life  is  never  long  enough.  It  is  only  in  such  cases  as 
those  formerly  quoted  from  Jevons,  that  examination  can  be 
exhaustive;  or  else  if  a  class  is  artificially  limited,  such  as,  'the 
present  House  of  Commons.'  There  perfect  induction  might 
show  (say)  that  every  member  has  two  Christian  names.  The 
argument  is  sometimes  exhibited  as  a  Syllogism  in  Darapti 
with  a  Minor  Premise  in  U.,  which  legitimates  a  Conclusion  in 
A.,  thus  : 

A.B.  to  Z  have  two  Christian  names; 

A.B.  to  Z  are  all  the  present  M.P.s : 
.*.  All  the  present  M.P.s  have  two  Christian  names. 
But  in  such  an  investigation  there  is  no  need  of  logical  method 
to  find  the  Major  Premise ;  it  is  mere  counting :  and  to  carry 
out   the  Syllogism  is  a   hollow  formality.     Accordingly,   our 


i66      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

definition  of  Induction  excludes  the  kind  unfortunately  called 
Perfect,  by  including  in  the  notion  of  Induction  a  reliance  on 
the  uniformity  of  nature ;  for  this  would  be  superfluous  if  every 
instance  in  question  had  been  severally  examined.  Imperfect 
Induction,  then,  is  what  we  have  to  deal  with  :  the  method  of 
showing  the  credibility  of  an  universal  real  proposition  by  an 
examination  of  some  of  the  instances  it  includes,  generally  a 
small  fraction  of  them. 

§  4.  Imperfect  Induction  is  either  Methodical  or  Imme- 
thodical.  Now  Method  is  procedure  upon  a  principle ;  and  if 
the  method  is  to  be  precise  or  conclusive,  the  principle  must 
be  precise  and  definite. 

There  is  a  Geometrical  method,  because  the  axioms  of 
Geometry  are  precise  and  definite,  and  by  their  means,  with 
the  aid  of  definitions,  laws  are  deduced  of  the  equality  of  lines 
and  angles  and  other  relations  of  position  and  magnitude  in 
space.  The  process  of  proof  is  purely  Deductive  (the  axioms 
and  definitions  being  granted).  Diagrams  are  used  not  as  facts 
for  observation,  but  merely  to  fix  our  attention  in  following  the 
general  argument ;  so  that  it  matters  little  how  badly  they  are 
drawn,  as  long  as  their  divergence  from  the  conditions  of  the 
proposition  to  be  proved  is  not  distracting.  Even  the  appeal 
to  *'  superposition  "  to  prove  the  equality  of  magnitudes  (as  in 
Euclid  I.  4),  is  not  an  appeal  to  observation,  but  to  our  judg- 
ment of  what  is  implied  in  the  foregoing  conditions.  Hence 
no  inference  is  required  from  the  special  case  to  all  similar 
ones ;  for  they  are  all  proved  at  once. 

There  is  also,  as  we  have  seen,  a  method  of  Deductive  Logic 
resting  on  the  principles  of  Consistency  and  the  Dictum  de 
omni  et  nuUo.  And  we  shall  find  that  there  is  a  method  of 
Inductive  Logic,  resting  on  the  principle  of  Causation. 

But  there  are  a  good  many  general  propositions,  more  or 
less  trustworthy  within  a  certain  range  of  conditions,  which 
cannot  be  methodically  proved  for  want  of  a  precise  principle 
by  which  they  may  be  tested  ;  and  they,  therefore,  depend 
upon  Immethodical  Induction,  that  is,  upon  the  examination 


^'^ 


INDUCTIVE   METHOD 


167 


i 


<• 


T 


i 


of  as  many  instances  as  can  be  found,  relying  for  the  rest  upon 
the  mere  undefinable  principle  of  the  Uniformity  of  Nature, 
since  we  are  not  able  to  connect  them  with  any  of  its  definite 
modes  enumerated  in  chap.  xiv.  §1.  To  this  subject  we  shall 
return  in  chap,  xix ,  after  treating  of  Methodical  Induction,  or 
the  means  of  determining  that  a  connection  of  events  is  of  the 
nature  of  Cause  and  Effect,  because  the  relation  can  be  shown 
to  have  the  marks  of  causation,  or  some  of  them. 

§  5.  Observations  and  Experiments  are  the  w^/^'/'/a/ grounds 
of  induction.  An  experiment  is  an  observation  made  under 
prepared,  and  therefore  known,  conditions ;  and,  when  obtain- 
able, it  is  much  to  be  preferred.  Simple  observation  shows 
that  the  burning  of  the  fire  depends,  for  one  thing,  on  the 
supply  of  air ;  but  it  cannot  show  us  that  it  depends  on  oxygen. 
To  prove  this  we  must  make  experiments ;  as  by  obtaining 
pure  oxygen  and  pure  nitrogen  (which,  mixed  in  the  proportion 
of  one  to  four,  form  the  air)  in  separate  vessels,  and  then 
plunging  a  burning  taper  into  the  oxygen — when  it  will  blaze 
fiercely,  and  again  plunging  it  into  the  nitrogen — when  it  will 
be  extinguished.  This  shows  that  the  greater  part  of  the  air 
does  nothing  to  keep  the  fire  alight,  except  by  diminishing  its 
intensity  and  so  making  it  last  longer.  Experiments,  now,  are 
more  perfect  the  more  carefully  they  are  prepared,  and  the  more 
completely  the  conditions  are  known  under  which  the  given 
phenomenon  is  to  be  observed.  Plainly,  however,  experiments 
are  only  possible  when  some  knowledge  has  already  been 
gained  by  observation,  or  else  the  preparation  which  they 
require  would  be  impossible. 

Observation,  then,  was  the  first  material  ground  of  induc- 
tion, and  in  some  sciences  it  remains  the  chief  ground.  The 
heavenly  bodies,  the  winds  and  tides,  the  strata  of  the  earth, 
and  the  movements  of  history,  are  beyond  our  power  to  experi- 
ment with.  Experiments  upon  the  living  body  or  mind  are 
indeed  resorted  to  when  practicable,  even  in  the  case  of  man, 
as  in  Psycho-physics,  and  the  investigation  of  Hypnotism ;  but, 
if  of  a  grave  nature,  they  are  usually  thought   unjustifiable. 


i68      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

And  in  political  affairs  experiments  are  hindered  by  the  reflec- 
tion, that  those  whose  interests  are  affected  must  bear  the  con- 
sequences and  may  resent  them.  Hence,  it  is  in  physical  and 
chemical  inquiries  that  direct  experiment  is  most  useful. 

Where  direct  experiment  is  possible,  however,  it  has  many 
advantages  over  unaided  observation.     If  one  experiment  does 
not  enable  us  to  observe  the  phenomenon  satisfactorily,  we 
may  try  again  and  again ;   whereas  the  mere  observer,  who 
wishes  to  study  the  bright  spots  on   Mars,  or  a  commercial 
crisis,  must  wait  for  a  favourable  opportunity.    Again,  in  making 
experiments  we  can  often  var}'the  conditions  of  the  phenomenon, 
so  as  to  observe  its  different  behaviour  in  each  case :  whereas 
he  who  depends  solely  on  observation  must  trust  the  bounty 
of  nature  to  supply  him  with  a  suitable  diversity  of  instances. 
It  is  a  particular  advantage  of  experiment  that  a  phenomenon 
may  sometimes  be  "isolated,"  that  is,  removed  from  the  influ- 
ence of  all  agents  except  that  whose  operation  we  desire  to 
observe,  or  except  those  whose  operation   is  already  known  : 
whereas  a  simple  observer,  who  has  no  control  over  the  con- 
ditions of  the  subject  he  studies,  can  never  be  quite  sure  that 
its  movements  or  changes  are  not  due  to  causes  that  have 
never  been  conspicuous  enough  to  draw  his  attention.    Finally, 
experiment  enables  us  to  observe  coolly  and  circumspectly  and 
to  be  precise  as  to  what  happens,  the  time  of  its  occurrence,  the 
order  of  successive  events,  their  duration,  intensity  and  extent. 
§  6.  The  principle  of  Causation  is  the  for7tial  ground   of 
Induction;  and   the  Inductive  Canons   derived   from    it   are 
means  of  testing  the   formal    sufficiency  of  observations   to 
justify   the   statement   of    a   Law.      If  we   can    observe   the 
process  of  cause  and  effect  in  nature  we  may  generalise  our 
observation  into   a  law,  because   that   process   is   invariable. 
First,  then,  can  we  observe  the  course  of  cause  and  effect  ? 
Our  power  to  do  so  is  plainly  limited  by  the  refinement  of  our 
senses,  aided  by  instruments  such  as   lenses,  thermometers, 
balances,  etc.     If  the  causal  process  is  essentially  molecular 
change,  as  in  the  maintenance  of  combustion  by  oxygen,  we 


INDUCTIVE   METHOD 


169 


^( 


cannot  directly  observe  it ;  if  the  process  is  partly  cerebral  or 
mental,  as  in  social  movements  which  depend  on  feeling  and 
opinion,  it  can  but  remotely  be  inferred  ;  even  if  the  process  is  a 

collision  of  moving  masses  (billiard-balls),  we  cannot  really  observe 
what  happens,  the  elastic  yielding  and  recoil  and  the  internal 
changes  that  result ;  though  no  doubt  photography  will  throw 
some  light  upon  this,  as  it  has  done  upon  the  galloping  of 
horses  and  the  impact  of  projectiles.  Direct  observation  is 
limited  to  the  effect  which  any  change  in  a  phenomenon  (or  its 
index)  produces  upon  our  senses ;  and  what  we  believe  to  be 
the  causal  process  is  a  matter  of  inference  and  calculation.  It 
is  to  be  regretted,  if  the  meagre  and  abstract  outlines  of  Induc- 
tive Logic  foster  the  notion,  that  the  evidence  on  which  Science 
(or  even  common  opinion)  rests  is  simple:  it  is  amazingly 
intricate  and  cumulative. 

Secondly,  then,   so  far  as  we  can  observe  the  process  of 
nature,  how  shall  we  judge  whether  a  relation  of  Cause  and 
Effect  is  before  us  ?     By  looking  for  the  five  marks  of  Causa- 
tion.    Thus,  in  the  experiment  above  described,  showing  that 
oxygen   supports   combustion,    we    find— (i)   that    the    taper 
which   only  glowed   before  being   plunged    into   the  oxygen, 
bursts  into  flame  when  there— Sequence ;  (2)  that  this  begins 
to  happen  at  once  without  perceptible  interval — Immediacy ; 
(3)  that  no  other  agent  or  disturbing  circumstance  was  present 
(the  preparation  of  the  experiment  having  excluded  any  such 
thing)— Unconditionalness;  (4)  the  experiment  may  be  repeated 
as  often  as  we  like  with  the  same  result — Invariableness.     In- 
variableness,  indeed,  I  do  not  regard  as  formally  necessary  to 
be  shown,  supposing  the  other  marks  to  be  clear;  for  it  can 
only  be  proved  within  our  experience ;  and  the  very  object  of 
Induction  is  to  find  grounds  of  belief  beyond  actual  experience. 
However,  for  material  assurance,  to  guard  against  his  ow^n  liability 
to  error,  the  inquirer  will  of  course  repeat  his  experiments. 

The  above  four  are  the  qualitative  marks  of  Causation  : 
the  fifth  and  quantitative  mark  is  the  Equality  of  Cause  and 
Effect ;  and  this,  in  the  above  example,  the  Chemist  deter- 


I70      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

mines  by  showing,  that  instead  of  the  oxygen  and  wood  that 
have  disappeared  during  combustion,  an  equivalent  amount  of 
carbonic  acid,  water,  etc.,  has  been  formed. 

Here,  then,  we  have  all  the  marks  of  Causation ;  but  in  the 
ordinary  judgments  of  life,  in  history,  politics,  criticism,  busi- 
ness, we  must  not  expect  such  clear  and  direct  proofs ;  and  we 
shall  see  in  subsequent  chapters  how  different  kinds  of  evidence 
are  combined  in  different  departments  of  investigation. 

§  7.  The  Inductive  Canons,  to  be  explained  in  the  next 
chapter,  describe  the  character  of  observations  and  experiments 
that  justify  us  in  drawing  conclusions  about  Causation ;  and, 
as  we  have  observed,  they  are  derived  from  the  principle  of 
Causation  itself.  According  to  that  principle,  cause  and  effect 
are  invariably,  immediately  and  unconditionally  antecedent  and 
consequent,  and  are  equal  as  to  the  matter  and  energy  embodied. 

Invariability  can  only  be  observed,  in  any  of  the  methods  of 
induction,  by  collecting  more  and  more  instances,  or  repeating 
experiments.     Of  course  it  can  never  be  exhaustively  observed. 

Immediacy  is  also,  in  direct  induction,  a  matter  for  the  most 
exact  observation  that  is  possible. 

Succession,  or  the  relation  itself  of  antecedent  and  conse- 
quent, must  either  be  directly  observed  ;  or  else  ascertained  by 
showing  that  energy  gained  by  one  phenomenon  has  been  lost 
by  another,  for  this  implies  succession. 

But  the  Unconditionality  of  Causation  it  is  the  great  object 
of  the  methods  to  determine,  and  for  that  purpose  its  meaning 
may  be  further  explicated  by  the  following  rules : 

I. — For  Positive  Instances. 

To  find  a  Cause :  (a)  Any  agent  whose  introduction  among 
certain  conditions  (without  further  change)  is  followed  by  a 
given  phenomenon ;  or,  (b)  whose  removal  is  followed  by  the 
ce«isation  (or  modification)  of  that  phenomenon,  is  (so  far)  the 
cause  or  an  indispensable  condition  of  it. 

To  find  the  Effect :  (r)  Any  event  that  follows  a  given 
phenomenon,  when  there  is  no  further  change ;   or,  (d)  that 


INDUCTIVE   METHOD 


171 


1 


>' 


V 


does  not  occur  w^hen  the  conditions  of  a  former  occurrence  are 
exactly  the  same,  except  for  the  absence  of  that  phenomenon, 
is  the  effect  of  it  (or  is  dependent  on  it). 

II. — For  Negative  Instances. 

To  exclude  a  supposed  Cause :  (a)  Any  agent  that  can  be 
introduced  among  certain  conditions  without  being  followed 
by  a  given  phenomenon  (or  that  is  found  without  that  pheno- 
menon) ;  or  (b)  that  can  be  removed  when  that  phenomenon 
is  present  without  impairing  it  (or  that  is  absent  when  that 
phenomenon  is  present),  is  not  the  cause,  or  does  not  com- 
plete the  cause,  of  that  phenomenon  in  those  circumstances. 

To  exclude  a  supposed  Effect:  (r)  Any  event  that  occurs 
without  the  introduction  (or  presence)  of  a  given  phenomenon  ; 
or  (d)  that  does  not  occur  w^hen  that  phenomenon  is  introduced 
(or  is  present),  is  not  the  effect  of  that  phenomenon. 

Subject  to  the  conditions  thus  somewhat  cumbrously  stated, 
the  rules  may  be  briefly  put  as  follows : 

I.  (a)  That  which  (without  further  change)  is  followed  by  a 
given  event  is  its  cause. 

II.  {a)  That  which  is  not  so  followed  is  not  the  cause. 

I.  (b)  That  which  cannot  be  left  out  without  impairing  a 
phenomenon  is  a  condition  of  it. 

II.  (b)  That  which  can  be  left  out  is  not  a  condition  of  it. 
Again,  the  Equality  of  Cause  and  Effect  may  be   further 

explained  by  these  rules  : 

III.  {a)  When  a  cause  (or  effect)  increases  or  decreases,  so 
does  its  effect  (or  cause). 

III.  (b)  If  two  phenomena,  having  the  other  marks  of  cause 
and  effect,  seem  unequal,  the  less  contains  an  unexplored  factor. 

III.  (c)  If  an  antecedent  and  consequent  do  not  increase  or 
decrease  correspondingly,  they  are  not  cause  and  effect,  so  far 
as  they  vary. 

It  will  next  be  shown  that  these  propositions  are  vaiiously 
combined  in  Mill's  five  Canons  of  Induction. 


CHAPTER  XVI 
THE   CANONS   OF   DIRECT   INDUCTION 

§  I.  Let  me  begin  by  borrowing  an  example  from  Professor 
Bain  {Logic :  B.  III.  c.  6).     The  North-East  wind  is  generally 
detested  in  this  country :  as  long  as  it  blows  few  people  feel 
at  their  best.     Occasional  well-known  causes  of  a  wind  being 
injurious,  are  violence,  excessive  heat  or  cold,  excessive  dryness 
or  moisture,   electrical  condition,    want    of  ozone,   the   being 
laden  with  dust  or  exhalations.     Let  the  hypothesis  be  that 
the  last  is  the  cause  of  the  North-East  wind's  unwholesome 
quality;  since  we  know  it  is  a  ground  current  setting  from  the 
pole  toward  the  equator  and  bent  westward  by  the  rotation  of 
the  earth  ;  so  that,  reaching  us  over  thousands  of  miles  of  land, 
it  may  well  be  fraught  with  dust,  effluvia  and  microbes.     Now' 
examining  many  cases  of  North-East  wind,  we  find  that  this  is 
the  only  circumstance  in  which  all  the  instances  agree :  for  it 
is  sometimes  cold,  sometimes  hot ;  generally  dry,  but  some- 
times wet ;  sometimes  light,  sometimes  violent;  of  all  electrical 
conditions,  and  is  charged  with  ozone  on  the  Norfolk  coast. 
Each  of  the  other  circumstances,  then,  can  be  omitted  without 
the  N.E.  wind  ceasing  to  be  noxious;  but  one  circumstance  is 
never   absent,    namely,    that   it   is   a   ground   current.     That 
circumstance,  therefore,  is  probably  the  Cause  of  its  injurious- 
ness.     This  case  illustrates  : — 

(i)  The  Canon  of  Agreement. 
If  two  or  more  instances  of  a  phenomenon  under  investigation 
have  only  one  other  circumstance  (antecedent  or  consequent)  in 


K 


V 


X 


THE   CANONS   OF   DIRECT   INDUCTION      173 

common^  that  circumstance  is  the  cause  {or  an  indispensable  part 
of  the  cause)  or  the  effect  of  the  phenomenon. 

This  rule  of  proof  (so  far  as  it  is  used  to  establish  direct 
causation)  depends  first,  upon  observation  of  an  invariable 
connection  between  the  given  phenomenon  and  one  other 
circumstance  ;  and,  secondly,  upon  1.  (a)  and  II.  {b)  among  the 
propositions  obtained  from  the  unconditionality  of  causation  at 
the  close  of  the  last  chapter. 

Let  us  suppose  two  instances  of  the  occurrence  of  a  given 
phenomenon.      A,  an  antecedent,  or  /,  a  consequent,  with 
concomitant  facts  or  events,  and  let  us  represent  them  thus  : — 
ABC  A  D  E  (antecedents) 

p  q  r  p  s   t  (consequents) ; 

and  let  us  suppose  that,  in  this  case,  the  immediate  succession 
of  events  can  be  observed.  Then  A  is  the  cause  of/.  For, 
as  far  as  our  instances  go,  A  is  the  invariable  antecedent  of  /  ; 
and  /  is  the  invariable  consequent  of  A.  But  the  two  instances 
of  A  or  /  agree  in  no  other  circumstance.  Therefore  A  is  (or 
completes)  the  unconditional  antecedent  of  /.  For  B  and  C 
are  not  the  causes  of  /,  being  absent  in  the  second  instance 
(Rule  II.  {b))\  nor  are  D  and  E,  being  absent  in  the  first 
instance.  Moreover,  q  ana  r  are  not  Effects  of  A,  being 
absent  in  the  second  instance  (Rule  11.  (^));  nor  are  s  and  /, 
being  absent  in  the  first  instance. 

It  should  be  observed  that  the  cogency  of  the  proof  depends 
entirely  upon  its  tending  to  show  the  unconditionality  of  the 
sequence  A-/.  That/  follows  A  even  immediately,  is  nothing 
by  itself :  if  a  man  sits  down  to  study  and,  on  the  instant,  a 
hand-organ  begins  under  his  window,  he  must  not  infer  malice 
in  the  musician  :  thousands  of  things  follow  one  another  every 
moment  without  traceable  connection ;  and  this  we  call  '  acci- 
dental.' Even  invariable  sequence  is  not  enough  to  prove 
direct  causation  ;  for,  in  our  experience,  does  not  night  invari- 
ably follow  day?  The  proof  requires  that  the  instances  be 
such  as  to  show  not  merely  what  events  are  m  invariable 
sequence,  but  also  what  are  not.     From  among  the  occasional 


/^ 


174      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

antecedents  of  p  (or  consequents  of  A)  we  have  to  eliminate 
the  accidental  ones.  And  this  is  done  by  finding  or  making 
'negative  instances'  in  respect  of  each  of  them.     Thus  the 

A  D  E   .  .      . 

mstance   p   ^  ^    is  a  negative  mstance  of  B  and  C  considered 

as  supposable  causes  of  /  (and  of  q  and  r  as  supposable 
effects  of  A) ;  for  it  shows  that  they  are  absent  when/  (or  A) 
is  present. 

To  insist  upon  the  cogency  of  *  negative  instances'  was 
Bacon's  great  contribution  to  Inductive  Logic.  If  we  neglect 
them,  and  merely  collect  examples  of  the  sequence  A  -/,  this  is 
*  simple  enumeration  ' ;  and  although  simple  enumeration,  when 
the  instances  of  agreement  are  numerous  enough,  may  give 
rise  to  a  strong  belief  in  the  connection  of  phenomena,  yet  it 
can  never  be  a  methodical  or  logical  proof  of  causation,  since 
it  does  not  indicate  the  unconditionalness  of  the  sequence. 
For  simple  enumeration  of  the  sequence  A-/  leaves  open  the 
possibility  that,  besides  A,  there  is  always  some  other  antecedent 
of/,  say  X ;  and  then  X  may  be  the  cause  of/.  To  disprove 
It,  we  must  find,  or  make,  a  negative  instance  of  X— where 
/  occurs,  but  X  is  absent. 

If  indeed  (or  whenever)  we  recognise  the  possibility  of  a 
Plurality  of  Causes,  this  method  of  Agreement  cannot  be  quite 
satisfactory.  For  then,  in  such  instances  as  the  above,  although 
D  is  absent  in  the  first,  and  B  in  the  second,  it  does  not 
follow  that  they  are  not  the  causes  of  / ;  for  they  may  be 
alternative  causes  :  B  may  have  produced  p  in  the  first  instance, 
and  D  in  the  second ;  A  being  in  both  cases  an  accidental 
circumstance  in  relation  to/.  To  remedy  this  shortcoming  by 
the  method  of  Agreement  itself  (we  shall  see  other  remedies 
hereafter)  the  only  course  is  to  find  more  instances  of  /. 
We  may  never  find  a  negative  instance  of  A  ;  and,  if  not,  the 
probability  that  A  is  the  cause  of  /  increases  with  the  number 
of  instances.  But  if  there  be  no  antecedent  that  we  cannot 
sometimes  exclude,  yet  the  collection  of  instances  will  probably 
give  at  last  all  the  causes  of//  and  by  finding  the  proportion 


\ 


5 


THE   CANONS   OF   DIRECT   INDUCTION      175 

of  instances  in  which  A,  B,  or  X  precedes/,  we  may  estimate 
the  probability  of  any  one  of  them  being  the  cause  of  /  in  any 
given  case  of  its  occurrence. 

Again,  though  we  have  assumed  that,  in  the  instances 
supposed  above,  immediate  sequence  is  observable,  yet  in 
many  cases  it  may  not  be  so,  if  we  rely  only  on  the  canon  of 
Agreement;  if  instances  cannot  be  obtained  by  experiment, 
and  we  have  to  depend  on  observation.  The  phenomena  may 
then  be  so  mixed  together  that  A  and  /  seem  to  be  merely 
concomitant ;  so  that,  though  connection  of  some  sort  may  be 
rendered  highly  probable,  we  may  not  be  able  to  say  which  is 
Cause  and  which  is  Effect,  We  must  then  try  (as  Bain  says) 
to  trace  the  expenditure  of  energy  :  if  /  gains  when  A  loses, 
the  course  of  events  is  from  A  to/;  but  here  we  are  anticipa- 
ting the  method  of  Variations  (§  4). 

Moreover,  where  succession  cannot  be  traced,  the  method 
of  Agreement  may  point  to  a  connection  between  two  facts 
(perhaps  as  joint-effects  of  a  remote  cause)  where  direct  causa- 
tion seems  to  be  out  of  the  question :  e.g.^  that  Negroes, 
though  of  different  tribes,  different  localities,  customs,  etc.^  are 
both  prognathous  and  dolichocephalic.  But  such  an  investiga- 
tion belongs  to  the  theory  of  Definition  rather  than  to  our 
present  subject. 

Men  often  use  arguments  which,  if  they  knew  it,  might  be  shown  to 
conform  more  or  less  to  this  canon  ;  for  they  collect  many  instances  to 
show  that  two  events  are  connected  ;  but  usually  neglect  to  bring  out 
the  negative  side  of  their  proof ;  so  that  their  arguments  only  amount 
to  simple  enumeration.  Thus  Ascham  in  his  Toxophilus,  insisting  on 
the  national  importance  of  archery,  argues  that  victory  has  always 
depended  on  superiority  in  shooting;  and,  to  prove  it,  he  shows  how 
the  Parthians  checked  the  Romans,  Sesostris  conquered  great  part  of 
the  known  world,  Tiberius  overcame  Arminius,  the  Turks  established 
their  empire,  and  the  English  defeated  the  French  (with  many  like 
examples)— all  by  superior  archery.  But  having  cited  these  cases  to' 
his  purpose,  he  is  content ;  whereas  he  might  have  greatly  strengthened 
his  proof  by  showing  how  one  or  the  other  instance  excludes  other 
possible  causes  of  success.  Thus  :  the  cause  was  not  discipline,  for  the 
Romans  were  better  disciphned  than  the  Parthians  ;  nor  yet  the  boasted 
superiority  of  a  northern  habitat,  for  Sesostris  issued  from  the  south ; 


176      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

nor  better  manhood,  for  here  the  Germans  probably  had  the  advantage 
ot  the  Romans ;  nor  superior  civiUsation.  for  the  Turks  were  lels 
civihsed  than  most  of  those  they  conquered  ;  nor  numbers,  nor  even 
a  good  cause,  for  the  French  were  more  numerous  than  the  Enghsh 
and  were  shamefully  attacked  by  Henry  V.  on  their  own  soil.  Many 
an  argument  from  simple  enumeration  may  thus  be  turned  into  an 
mduction  of  greater  plausibility  according  to  the  canon  of  Agreement 

Still,  in  the  above  case,  the  effect  (victory)  is  so  vaguely  conceived. 

that  a  plurality  of  causes  must  be  allowed  for :  although,  e.g.,  discipline 

did  not  enable  the  Romans  to  conquer  the  Parthians.  it  may  have  been 

heir  chief  advantage  over  the  Germans  ;  and  it  was  certainly  important 

to  the  English  under  Henry  V.  in  their  war  with  the  French. 

Here  is  another    argument,  somewhat    similar    to    the    above    put 
forward  by  Mr.  Spencer  with  a  full  consciousness  oAts  logical  character 
States   that  make  war    their  chief  object,  he  says,  assume  a  certain 
type  of  organisation,  involving  the  growth  of  the  warrior  class  and  the 
treatment  of  labourers  as  existing  solely  to  sustain  the  warriors  •  the 
complete  subordination  of  individuals  to  the  will  of  the  despotic  soldier- 
king,  their  property,  liberty  and  life  being  at  the  service  of  the  State  • 
the  regimentation  of  society  not  only  for  military  but  also  for  civil 
purposes ;  the  suppression  of  all  private  associations,  etc.     This  is  the 
case  in  Dahomey  and  in  Russia,  and  it  was  so  at  Sparta,  in  Egypt  and 
in  the  empire  of  the  Yncas.     But  the  similarity  of  organisation  in  ihese 
States  cannot  have  been  due  to  race,  for  they  are  all  of  different  races  • 
nor  to  size,  for  some  are  small,  some  large ;  nor  to  climate  or  other 
circumstances  of  habitat,  for  here  again  they  differ  widely  •    the  one 
thing  they  have  in  common  is  the  military  purpose ;  and  this,  therefore 
must  be  the  cause  of  their  similar  organisation.     ^Political  Institutions  )  ' 
By  this  method,  then,  to  prove  that  one  thing  is  causally  connected 
with  another,  say  A  with/,  we  show  first,  that  in  all  instances  of />   A  is 
present ;  and.  secondly,  that  any  other  supposable  cause  of  t  may  be 
absent  without  disturbing  p.     We  next  come  to  a  method  the  use  of 
which  greatly  strengthens  the  foregoing,   by  showing  that  where  b  is 
absent  A  is  also  absent,  and  (if  possible)  that  A  is  the  only  supposable 
cause  that  is  always  absent  along  with  /. 

§  2.  The  CanOx\  of  the  Joint  Method  of  Agree- 
ment IN  Presence  and  in  Absence. 
If  {\)  two  or  more  instances  in  which  a  phenomenon  occurs 
have  only  one  other  circumstance  {antecedent  or  consequent)  in 
common,  while  (2)  two  or  more  instances  in  which  it  does  not 
occur  {though  in  some  important  points  they  resemble  the  former 
set  of  instances)  have  nothing  else  in  common  save  the  absence  of 


THE   CANONS   OF   DIRECT   INDUCTION      177 

that  circumstance — the  circu?tistance  in  which  alone  the  two  sets, 
of  instances  differ  throughout  {being  present  in  the  first  set  and^ 
absent  in  the  second)  is  the  effect  or  the  cause,  or  an  indispensable  ■ 
part  of  the  cause,  of  the  pheno??ienon. 

The  first  clause  of  this  Canon  is  the  same  as  that  of  the  . 
Method  of  Agreement,  and  its  significance  depends  upon  the. 
same  propositions  concerning  Causation.     The  second  clause, 
relating   to   instances  in  which   the   phenomenon   is   absent, 
depends  for  its  probative  force  upon  Prop.  II.  {a\  and  I.  {b). 
Let  the  two  sets  of  instances  be  represented  as  follows : 


Instances  of  Presence. 

ABC 

p  q   r 

A  D  E, 

p   s   t 

AFG      .      ^ 

p  u  v 


Instances  of  Absence. 

C  HF 

r  X  IV 

B  D  K 

q  y   z 

EG  M 

//  n 


Then  A  is  the  cause  of/,  or  /  the  effect  of  A  :  first,  by  the  Canon, 
of  Agreement  in  Presence,  as  represented  by  the  first  set  of. 
instances;  and,  secondly,  by  Agreement  in  Absence  in  the. 
second  set  of  instances.     For  there  we  see  that  C  H  F  B  D  K . 
E  G  M  occur  without  the  phenomenon  /,  and  therefore  (by. 
Prop.  II.  {a) )  are  not  its  cause,  or  not  the  whole  cause,  unless, 
they  have  been  counteracted   (which  is   a   point  for  further, 
investigation).    We  also  see  that  r  x  iv  q  y  z  t  f  n  occur  without . 
A,  and  therefore  are  not  the  effects  of  A.     And,  further,  if  the . 
negative   instances  represent  all  possible  cases,   we  see  that, 
(according  to  Prop.  I.  {b) )  A  is  the  cause  of/,  because  it  cannot . 
be  omitted  without  the  cessation  of  p.     The  inference  that  A . 
and/  are  Cause  and  Effect,  suggested  by  their  being  present, 
throughout  the  first  set  of  instances,  is  therefore  strengthened, 
by  their  being  both  absent  throughout  the  second  set. , 

As  this  Double  Method,  like  the  Single  Method  of  Agree, 
ment,  relies  mainly  on  observation.  Sequence  may  not  be  per- 


178      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

ceptible  in  the  instances  observed,  and  then,  direct  causation 
cannot  be  proved  by  it,  but  only  the  probability  of  causal  con- 
nection. It  has,  however,  one  peculiar  advantage,  namely, 
that  if  the  second  list  of  instances  (in  which  the  phenomenon 
and  its  supposed  antecedent  are  both  absent)  can  be  made 
exhaustive,  it  precludes  any  hypothesis  of  a  plurality  of  causes  ; 
since  all  possible  antecedents  will  have  been  included  in  this 
list  without  producing  the  phenomenon.  Thus,  in  the  above 
symbolic  example,  taking  the  first  set  of  instances,  the  suppo- 
sition is  left  open  that  B,  C,  D,  E,  F,  G,  may,  at  one  time  or 
another,  have  been  the  cause  of  /  /  but,  in  the  second  list, 
these  antecedents  all  occur  here  or  there  without  producing/, 
and  therefore  (unless  counteracted  in  some  way)  cannot  be  the 
cause  of/.  A,  then,  stands  out  as  the  one  thing  that  is  present 
whenever/  is  present,  and  absent  whenever/  is  absent. 

Stated  in  this  abstract  way,  the  Double  Method  may  seem  very 
elaborate,  compHcated  and  difficult ;  yet,  in  fact,  we  all  use  it  in  our 
ordinary  reasonings.  If  a  man  finds  that  whenever  he  eats  cucumber 
he  suffers  from  indigestion,  this  indicates  by  Agreement  that  cucumber 
is  the  cause  of  his  pain.  But,  if  he  is  fond  of  cucumber,  he  will  put 
the  fault  upon  other  ingredients  of  his  diet  taken  at  the  same  time,  such 
as  cheese,  salmon  or  pastry,  which  he  likes  less.  Making,  however,  a 
second  list  of  dinners  (say)  when  visiting,  at  which  cucumber  is  not 
served,  whilst  cheese,  salmon,  pastry,  etc.,  all  occur,  and  finding  that  he 
does  not  suffer  from  indigestion,  the  conclusion  seems  to  be  forced  upon 
him  that  cucumber  is  the  only  pleasure  of  the  table  that  must  be 
bought  with  pain.  In  this  case  sequence  can  be  observed.  Again,  if, 
whilst  a  certain  oarsman  is  stroke  of  a  boat  whose  crew  often  changes, 
it  always  wins;  whilst,  after  he  retires,  it  always  loses  (in  spite  of 
other  changes) ;  his  admirers  will  certainly  argue  according  to  this 
Method  that,  since  his  presence  brought  victory  and  his  absence  brings 
defeat,  success  was  due  to  him  and  to  him  alone. 

There  are  some  instructive  applications  of  this  Double  Method  in  Dr. 
Wallace's  Darwinism.  In  chap,  viii.,  for  example,  on  Colour  in  Animals, 
he  observes,  that  the  usefulness  of  their  colouration  to  animals  is  shown 
by  the  fact  that,  "  as  a  rule,  colour  and  marking  are  constant  in  each 
species  of  wild  animal,  while,  in  almost  every  domesticated  animal 
there  arises  great  variability.  We  see  this  in  our  horses  and  cattle,  our 
dogs  and  cats,  our  pigeons  and  poultry.  Now  the  essential  difference 
between  the  conditions  of  life  of  domesticated  and  wild  animals  is,  that 


t 


THE   CANONS   OF   DIRECT   INDUCTION     179 

the  former  are  protected  by  man,  while  the  latter  have  to  protect  them- 
selves."     Wild   animals    protect    themselves    by  acquiring    qualities 
adapted  to  their  mode  of  life.     Now  colouration  is  a  very  important 
quality,  its  chief,  though  not  its  only  use,  being  concealment.     Hence 
a  useful  colouration  having  been  established  in  any  species,  though 
mdividuals  may  occasionally  vary  from  it,  they  will  generally  perish ; 
whilst  among  domestic  animals  variation  of  colour  or  marking  is  subject 
to  no  check  except  the  taste  of  owners.     We  have,  then,  two  lists  of 
instances :    first,  innumerable  species  of  wild   animals  in  which  the 
colouration  is  constant  and  which  depend  upon  their  own  qualities  for 
existence ;  secondly,  several  species  of  domestic  animals  in  which  the 
colouration  is  not  constant,  and  which  do  not  depend  upon  their  own 
qualities  for  existence.    In  the  former  list  two  circumstances  are  present 
together  (under  all  sorts  of  conditions) ;  in  the  latter  they  are  absent 
together.     The   argument   may  be   further  strengthened  by  adding  a 
third  list,  parallel  to  the  first,  comprising  domestic  animals  in  which 
colouration  is  approximately  constant,  but  where  (as  we  know)  it  is 
made  a  condition  of  existence  by  owners,  who  only  breed  from  those 
specimens  that  come  up  to  a  certain  standard  of  colouration. 

Dr.  Wallace  goes  on  to  discuss  the  colouring  of  arctic  animals  ;  I  will 
slightly  condense  his  statement.     In  the  arctic  regions  some  animals  are 
wholly  white  all  the  year  round,  such  as  the  polar  bear,  the  American 
polar  hare,  the  snowy  owl  and  the  Greenland  falcon  :  these  live  amidst 
almost   perpetual  snow.      Others,  who  live  where  the  snow  melts  in 
summer,  only  turn  white  in  winter,  such  as  the  arctic  hare,  the  arctic 
fox,   the   ermine   and   the   ptarmigan.     In   all   these   cases   the  white 
colouring  is  useful,  concealing  the  herbivores  from  their  enemies,  and 
also  the  carnivores  in  approaching  their  prey  ;  this  usefulness,  therefore, 
is  the  cause  of  the  white  colouring.     Two  other  explanations  have  how- 
ever been  suggested  :  first,  that  the  prevalent  white  of  the  arctic  regions 
directly  colours  the  animals,  either  by  some  photographic  or  chemical 
action  on  the  skin,  or  by  a  reflex  action  through  vision  (as  in  the 
chameleon) ;  secondly,  that  a  white  skin  checks  radiation  and  keeps  the 
animals  warm.     But  there  are  some  exceptions  to  the  rule  of  white 
colouring  in  arctic  animals  which  refute  these  hypotheses,  and  confirm 
the  author's.     The  sable  remains  brown  throughout  the  winter;  but  it 
frequents  trees,  with  whose  bark  its  colour  assimilates.    The  musk- 
sheep  is  brown  and  conspicuous ;  but  it  is  gregarious,  and  its  safety 
depends  upon   being  able  to  recognise  its  kind  and  keep  with  the  herd. 
The  raven  is  always  black ;  but  it  fears  no  enemy  and  feeds  on  carrion, 
and  therefore  does  not  need  concealment  for  either  defence  or  attack. 
The  colour  of  the  sable,  then,  though  not  white,  serves  for  concealment ; 
the  colour  of  the  musk-sheep  serves  a  purpose  more  important  than 
concealment;  the  raven  needs  no  concealment.     There  are  thus  two 
sets  of  instances:— in  one  set,  the  animals  are  white;  [a)  all  the  year- 


178      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

ceptible  in  the  instances  observed,  and  then,  direct  causation 
cannot  be  proved  by  it,  but  only  the  probability  of  causal  con- 
nection. It  has,  however,  one  peculiar  advantage,  namely, 
that  if  the  second  list  of  instances  (in  which  the  phenomenon 
and  its  supposed  antecedent  are  both  absent)  can  be  made 
exhaustive,  it  precludes  any  hypothesis  of  a  plurality  of  causes  ; 
since  all  possible  antecedents  will  have  been  included  in  this 
list  without  producing  the  phenomenon.  Thus,  in  the  above 
symbolic  example,  taking  the  first  set  of  instances,  the  suppo- 
sition is  left  open  that  B,  C,  D,  E,  F,  G,  may,  at  one  time  or 
another,  have  been  the  cause  of  / ;  but,  in  the  second  list, 
these  antecedents  all  occur  here  or  there  without  producing/, 
and  therefore  (unless  counteracted  in  some  way)  cannot  be  the 
cause  of/.  A,  then,  stands  out  as  the  one  thing  that  is  present 
whenever/  is  present,  and  absent  whenever/  is  absent. 

Stated  in  this  abstract  way,  the  Double  Method  may  seem  very 
elaborate,  complicated  and  difficult ;  yet,  in  fact,  we  all  use  it  in  our 
ordinary  reasonings.  If  a  man  finds  that  whenever  he  eats  cucumber 
he  suffers  from  indigestion,  this  indicates  by  Agreement  that  cucumber 
is  the  cause  of  his  pain.  But,  if  he  is  fond  of  cucumber,  he  will  put 
the  fault  upon  other  ingredients  of  his  diet  taken  at  the  same  time,  such 
as  cheese,  salmon  or  pastry,  which  he  likes  less.  Making,  however,  a 
second  list  of  dinners  (say)  when  visiting,  at  which  cucumber  is  not 
served,  whilst  cheese,  salmon,  pastry,  etc.,  all  occur,  and  finding  that  he 
does  7iot  suffer  from  indigestion,  the  conclusion  seems  to  be  forced  upon 
him  that  cucumber  is  the  only  pleasure  of  the  table  that  must  be 
bought  with  pain.  In  this  case  sequence  can  be  observed.  Again,  if, 
whilst  a  certain  oarsman  is  stroke  of  a  boat  whose  crew  often  changes, 
it  always  wins;  whilst,  after  he  retires,  it  always  loses  (in  spite  of 
other  changes);  his  admirers  will  certainly  argue  according  to  this 
Method  that,  since  his  presence  brought  victory  and  his  absence  brings 
defeat,  success  was  due  to  him  and  to  him  alone. 

There  are  some  instructive  appHcations  of  this  Double  Method  in  Dr. 
Wallace's  Darwinism.  In  chap,  viii.,  for  example,  on  Colour  in  Animals, 
he  observes,  that  the  usefulness  of  their  colouration  to  animals  is  shown 
by  the  fact  that,  "  as  a  rule,  colour  and  marking  are  constant  in  each 
species  of  wild  animal,  while,  in  almost  every  domesticated  animal 
there  arises  great  variability.  We  see  this  in  our  horses  and  cattle,  our 
dogs  and  cats,  our  pigeons  and  poultry.  Now  the  essential  difference 
between  the  conditions  of  Ufe  of  domesticated  and  wild  animals  is,  that 


THE   CANONS   OF   DIRECT   INDUCTION      179 

the  former  are  protected  by  man,  while  the  latter  have  to  protect  them- 
selves."     Wild   animals    protect    themselves    by   acquiring    qualities 
adapted  to  their  mode  of  life.     Now  colouration  is  a  very  important 
quality,  its  chief,  though  not  its  only  use,  being  concealment.     Hence 
a  useful  colouration  having  been  established  in  any  species,  though 
mdividuals  may  occasionally  vary  from  it,  they  will  generally  perish ; 
whilst  among  domestic  animals  variation  of  colour  or  marking  is  subject 
to  no  check  except  the  taste  of  owners.     We  have,  then,  two  lists  of 
instances:    first,   innumerable   species  of  wild   animals   in  which  the 
colouration  is  constant  and  which  depend  upon  their  own  qualities  for 
existence ;  secondly,  several  species  of  domestic  animals  in  which  the 
colouration  is  not  constant,  and  which  do  not  depend  upon  their  own 
qualities  for  existence.    In  the  former  list  two  circumstances  are  present 
together  (under  all  sorts  of  conditions) ;  in  the  latter  they  are  absent 
together.     The   argument   may  be   further  strengthened  by  adding  a 
third  list,  parallel  to  the  first,  comprising  domestic  animals  in  which 
colouration  is  approximately  constant,  but  where  (as  we  know)  it  is 
made  a  condition  of  existence  by  owners,  who  only  breed  from  those 
specimens  that  come  up  to  a  certain  standard  of  colouration. 

Dr.  Wallace  goes  on  to  discuss  the  colouring  of  arctic  animals  ;  I  will 
slightly  condense  his  statement.     In  the  arctic  regions  some  animals  are 
wholly  white  all  the  year  round,  such  as  the  polar  bear,  the  American 
polar  hare,  the  snowy  owl  and  the  Greenland  falcon  :  these  live  amidst 
almost   perpetual  snow.      Others,  who  live  where  the  snow  melts  in 
summer,  only  turn  white  in  winter,  such  as  the  arctic  hare,  the  arctic 
fox,   the  ermine  and   the  ptarmigan.     In   all   these  cases   the  white 
colouring  is  useful,  concealing  the  herbivores  from  their  enemies,  and 
also  the  carnivores  in  approaching  their  prey  ;  this  usefulness,  therefore, 
is  the  cause  of  the  white  colouring.     Two  other  explanations  have  how- 
ever been  suggested  :  first,  that  the  prevalent  white  of  the  arctic  regions 
directly  colours  the  animals,  either  by  some  photographic  or  chemical 
action  on  the  skin,  or  by  a  reflex  action  through  vision  (as  in  the 
chameleon) ;  secondly,  that  a  white  skin  checks  radiation  and  keeps  the 
animals  warm.     But  there  are  some  exceptions  to  the  rule  of  white 
colouring  in  arctic  animals  which  refute  these  hypotheses,  and  confirm 
the  author's.     The  sable  remains  brown  throughout  the  winter ;  but  it 
frequents  trees,  with  whose  bark  its   colour  assimilates.     The  musk- 
sheep  is  brown  and  conspicuous ;  but  it  is  gregarious,  and  its  safety 
depends  upon   being  able  to  recognise  its  kind  and  keep  with  the  herd. 
The  raven  is  always  black  ;  but  it  fears  no  enemy  and  feeds  on  carrion, 
and  therefore  does  not  need  concealment  for  either  defence  or  attack. 
The  colour  of  the  sable,  then,  though  not  white,  serves  for  concealment ; 
the  colour  of  the  musk-sheep  serves  a  purpose  more  important  than 
concealment;  the  raven  needs  no  concealment.     There  are  thus  two 
sets  of  instances:— in  one  set,  the  animals  are  white;  (a)  all  the  year; 


i8o      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

(6)  in  winter,  and  white  conceals  them  (a)  all  the  year,  (b)  in  winter; 
in  the  other  set.  the  animals  are  not  white,  and  to  them  either  whitenes' 
would  not  give  concealment,  or  concealment  would  not  be  advantageous. 
And  this  second  list  refutes  the  rival  hypothesis :  for  the  musk-sheep 
and  the  raven  are  as  much  exposed  to  the  glare  of  the  snow,  and  to  the 
cold,  as  the  other  animals  are. 

§  3.  The  Canon  of  Difference. 

//an  instance  in  ivhich  a  phenomenon  occurs,  and  an  instance 
tn  ivhich  it  does  not  occur,  have  every  other  circumstance  in 
common  save  one,  that  one  {whether  consequent  or  antecedent) 
occurring  only  in  the  former ;  the  circumstance  in  ivhich  alone 
the  two  instances  differ  is  the  effect,  or  the  cause,  or  an  indispen- 
sable condition  of  the  phenomenon. 

This  follows  from  Props.  I.  {a)  and  (b),  in  chapter  xv.  §  7. 

Let  two  instances,  such  as  the  Canon  requires,  be  represented 
thus : 

ABC  BC 

P  ^  r  g  r 

Then  A  is  the  cause  of/.  For,  in  the  first  instance,  A  being 
introduced  (without  further  change),  /  arises  (Prop  I.  (^) );  or, 
in  the  second  instance,  A  having  been  removed  (without  other 
change),/  disappears  (Prop.  I.  (b) ).  Similarly  we  may  prove, 
by  the  same  instances,  that/  is  the  effect  of  A. 

Which  of  two  phenomena  thus  shown  to  be  connected  is 
Cause,  and  which  Effect  (if  we  have  no  prior  knowledge  of 
their  nature,  and  are  not  experimenting,  but  relying  on  simple 
observation)  must  be  determined  by  observing  the  order  in 
which  they  occur ;  and  the  immediacy  of  their  connection  is 
also  a  matter  for  observation,  aided  by  whatever  instruments 
and  methods  of  inspection  and  measurement  may  be  available. 
As  to  the  invariability  of  the  connection,  it  may  of  course 
be  tested  by  collecting  more  instances  or  making  more  experi- 
ments ;  but  it  has  been  maintained,  that  a  single  experiment 
accordmg  to  this  method,  if  satisfactorily  performed,  is  suf- 
ficient  to   prove   causation,  and  therefore  implies    invariabi- 
lity (since  causation  is  unifor.n),  though  no  other   instances 


4  .-i^ 


THE   CANONS   OF   DIRECT   INDUCTION      181 

should  ever  be  obtainable;  because  a  single  perfect  experi- 
ment establishes  the  unconditionality  of  the  connection.  Now, 
formally  this  is  true;  but  in  any  actual  investigation  how 
shall  we  decide  what  is  a  satisfactory  or  perfect  experiment  ? 

Such  an  experiment  requires  that  in  the  negative  instance  —  , 

q  r 

B  C  shall  be  the  least  assemblage  of  conditions  necessary 
to  co-operate  with  A  in  producing/;  and  that  it  is  so  cannot 
be  ascertained  without  either  general  prior  knowledge  of  the 
nature  of  the  case  or  special  experiments  for  the  purpose.  So 
that  invariability  will  not  really  be  inferred  from  a  single  expe- 
riment ;  besides  that  every  prudent  inquirer  repeats  his  experi- 
ments, if  only  to  guard  against  his  own  liabihty  to  error. 

The  supposed  plurality  of  causes,  does  not  affect  the 
Method  of  Difference.  In  the  above  symbolic  case,  A  is 
clearly  one  cause  (or  condition)  of  /,  whatever  other  causes 
may  be  possible;  whereas  in  the  former  case  of  the  Single 
Method  of  Agreement,  it  remained  doubtful  (admitting  a 
plurality  of  causes)  whether  A,  in  spite  of  being  always 
present  with/,  was  ever  a  cause  or  condition  of  it. 

Now  this  Method  of  Difference  is  perhaps  oftener  than  any  other, 
though  without  our  being  distinctly  aware  of  it,  the  basis  of  ordinary 
judgments.  That  the  sun  gives  light  and  heat,  that  food  nourishes  and 
fire  burns,  that  a  stone  will  break  a  window  or  kill  a  bird,  that  turning 
a  tap  hastens  or  checks  the  flow  of  water  or  of  gas,  and  thousands  of 
other  propositions  are  known  to  be  true  by  rough  but  often  emphatic 
applications  of  this  method  in  common  experience. 

It  should  be  noticed  that  there  are  two  ways  in  which  this  application 
may  be  made  :  either  (a)  by  observation,  taking  for  our  two  instances 
distinct  assemblages  of  conditions,  differing  only  in  one*pkrticular  with 
its  antecedent  or  consequent ;  or  {h)  by  experiment,  regarding  as  our 
two  instances  the  same  assemblage  of  conditions,  before  and  after  the 
introduction  of  a  certain  agent.  If,  for  example,  there  are  two  men  of 
closely  similar  age,  health,  clothing  and  habits,  one  of  whom  stands  in 
the  shade  and  feels  cool,  whilst  the  other  stands  in  the  sun  and  feels 
warm,  this  shows  in  the  former  way,  by  observation,  that  the  sun  gives 
heat ;  but  if,  instead  of  this,  the  man  who  stands  in  th^shade  merely 
steps  into  the  sunshine  and  feels  warm,  the  same  proposition  is  proved 
in  the  latter  way  by  experiment.     The  experimental  way  is  the  better 


i8o      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

{b)  in  winter,  and  white  conceals  them  {a)  all  the  year,  {b)  in  winter ; 
in  the  other  set,  the  animals  are  ?wt  white,  and  to  them  either  whitenes 
would  not  give  concealment,  or  concealment  would  not  be  advantageous. 
And  this  second  list  refutes  the  rival  hypothesis  :  for  the  musk-sheep 
and  the  raven  are  as  much  exposed  to  the  glare  of  the  snow,  and  to  the 
cold,  as  the  other  animals  are. 

§  3.  The  Canon  of  Difference. 

Tfan  instance  in  ivhich  a  phenojnenon  occurs,  and  an  insfa?tce 
in  which  it  does  not  occur,  have  every  other  circumstance  in 
common  save  one,  that  o?te  {whether  consequent  or  antecedent) 
occurrifig  o?iiy  in  the  former ;  the  circumstaiice  in  which  aIo?te 
the  two  instances  differ  is  the  effect,  or  the  cause,  or  an  indispen- 
sable condition  of  the  phenomeno7i. 

This  follows  from  Props.  I.  {a)  and  (b),  in  chapter  xv.  §  7. 

Let  two  instances,  such  as  the  Canon  requires,  be  represented 

thus : 

ABC  BC 

p  q  r  q  r 

Then  A  is  the  cause  of/.     For,  in  the  first  instance,  A  being 

introduced  (without  further  change),/  arises  (Prop  I.  (a) );  or, 

in  the  second  instance,  A  having  been  removed  (without  other 

change),/  disappears  (Prop.  I.  (l))).     Similarly  we  may  prove, 

by  the  same  instances,  that/  is  the  effect  of  A. 

Which  of  two  phenomena  thus  shown  to  be  connected  is 
Cause,  and  which  Effect  (if  we  have  no  prior  knowledge  of 
their  nature,  and  are  not  experimenting,  but  relying  on  simple 
observation)  must  be  determined  by  observing  the  order  in 
which  they  occur ;  and  the  immediacy  of  their  connection  is 
also  a  matter  for  observation,  aided  by  whatever  instruments 
and  methods  of  inspection  and  measurement  may  be  available. 

As  to  the  invariability  of  the  connection,  it  may  of  course 
be  tested  by  collecting  more  instances  or  making  more  experi- 
ments ;  but  it  has  been  maintained,  that  a  single  experiment 
according  to  this  method,  if  satisfactorily  performed,  is  suf- 
ficient to  prove  causation,  and  therefore  implies  invariabi- 
lity (since  causation  is  unifor.n),  though  no  other   instances 


-ii»^ 


1 


THE   CANONS   OF   DIRECT   INDUCTION      181 

should  ever  be  obtainable ;  because  a  single  perfect  experi- 
ment establishes  the  unconditionality  of  the  connection.  Now, 
formally  this  is  true ;  but  in  any  actual  investigation  how 
shall  we  decide  what  is  a  satisfactory  or  perfect  experiment? 

R  C 

Such  an  experiment  requires  that  in  the  negative  instance > 

q  r 

B  C  shall  be  the  least  assemblage  of  conditions  necessary 
to  co-operate  with  A  in  producing/;  and  that  it  is  so  cannot 
be  ascertained  without  either  general  prior  knowledge  of  the 
nature  of  the  case  or  special  experiments  for  the  purpose.  So 
that  invariability  will  not  really  be  inferred  from  a  single  expe- 
riment j  besides  that  every  prudent  inquirer  repeats  his  experi- 
ments, if  only  to  guard  against  his  own  liability  to  error. 

The  supposed  plurality  of  causes,  does  not  affect  the 
Method  of  Difference.  In  the  above  symbolic  case,  A  is 
clearly  one  cause  (or  condition)  of  /,  whatever  other  causes 
may  be  possible ;  whereas  in  the  former  case  of  the  Single 
Method  of  Agreement,  it  remained  doubtful  (admitting  a 
plurality  of  causes)  whether  A,  in  spite  of  being  always 
present  with/,  was  ever  a  cause  or  condition  of  it. 

Now  this  Method  of  Difference  is  perhaps  oftener  than  any  other, 
though  without  our  being  distinctly  aware  of  it,  the  basis  of  ordinary 
judgments.  That  the  sun  gives  light  and  heat,  that  food  nourishes  and 
fire  burns,  that  a  stone  will  break  a  window  or  kill  a  bird,  that  turning 
a  tap  hastens  or  checks  the  flow  of  water  or  of  gas,  and  thousands  of 
other  propositions  are  known  to  be  true  by  rough  but  often  emphatic 
applications  of  this  method  in  common  experience. 

It  should  be  noticed  that  there  are  two  v%fays  in  which  this  application 
may  be  made  :  either  (a)  by  observation,  taking  for  our  two  instances 
distinct  assemblages  of  conditions,  differing  only  in  one|particular  with 
its  antecedent  or  consequent  ;  or  (6)  by  experiment,  regarding  as  our 
two  instances  the  same  assemblage  of  conditions,  before  and  after  the 
introduction  of  a  certain  agent.  If,  for  example,  there  are  two  men  of 
closely  similar  age,  health,  clothing  and  habits,  one  of  whom  stands  in 
the  shade  and  feels  cool,  whilst  the  other  stands  in  the  sun  and  feels 
warm,  this  shows  in  the  former  way,  by  observation,  that  the  sun  gives 
heat ;  but  if,  instead  of  this,  the  man  who  stands  in  th^shade  merely 
steps  into  the  sunshine  and  feels  warm,  the  same  proposition  is  proved 
in  the  latter  way  by  experiment.     The  experimental  way  is  the  better 


i82      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

when,  as  in  this  case,  an  immediate  sequence  can  be  obtained,  because 
it  gives  a  greater  certainty  of  there  being  no  difference  between  the  two 
instances  except  the  intervention  of  the  given  agent.  For  when  there 
are  two  separate  sets  of  conditions,  it  may  be  very  difficuU  to  make  sure 
that  they  are  exactly  similar  except  in  one  circumstance  with  its  ante- 
cedent or  consequent.  On  the  other  hand,  the  experimental  method  is 
unsatisfactory  if  some  time  must  elapse  between  the  introduction  of  the 
agent  and  the  manifestation  of  its  effects ;  for  then  other  changes  may 
have  occurred  meanwhile  to  which  these  effects  are  really  due.  If  you 
throw  a  stone  at  a  window  and  the  window  breaks  (nothing  else  having 
happened  apparently),  it  will  be  thought  pretty  clear  that  the  missile 
was  the  immediate  unconditional  antecedent  of  the  fracture :  but  if, 
feeling  out  of  sorts,  you  take  a  drug  and  some  time  afterwards  feel 
better,  it  is  not  clear  on  this  ground  alone  that  the  drug  was  the  cause 
of  recovery,  for  other  curative  processes  may  have  been  active  mean- 
while— food,  or  sleep,  or  exercise. 

Any  book  on  some  branch  of  Physics  or  on  Chemistry  will  furnish 
scores  of  examples  of  the  Method  of  Difference  ;  such  as  Galileo's  ex- 
periment to  show  that  air  has  weight,  by  first  weighing  a  vessel  filled 
with  ordinary  air,  and  then  filling  it  with  condensed  air  and  weighing  it 
again ;  when  the  increased  weight  can  only  be  due  to  the  greater 
quantity  of  air  contained.  The  melting-point  of  solids  is  determined  by 
heating  them  until  they  do  melt  (as  silver  at  looo^  C,  gold  at  1250°, 
platinum  at  2000°) ;  for  the  only  difference  between  bodies  at  the  time 
of  melting  and  just  before  is  the  addition  of  so  much  heat.  Similarly 
with  the  boiling-point  of  liquids.  That  the  transmission  of  sound 
depends  upon  the  continuity  of  an  elastic  ponderable  medium,  is  proved 
by  letting  a  clock  strike  in  a  vacuum  (under  a  glass  from  which  the  air 
has  been  withdrawn  by  an  air-pump),  and  standing  upon  a  non-elastic 
pedestal :  when  the  clock  may  be  seen  to  strike,  but  makes  only  such  a 
faint  sound  as  may  be  due  to  the  imperfections  of  the  vacuum  and  the 
pedestal. 

The  experiments  by  which  the  chemical  analysis  or  synthesis  of 
various  forms  of  matter  is  demonstrated,  are  simple  or  compound  appli- 
cations of  this  Method  of  Difference,  together  with  the  quantitative 
mark  of  causation  (that  cause  and  effect  are  equal) ;  since  the  bodies 
resulting  from  an  analysis  are  equal  in  weight  to  the  body  analysed, 
and  the  body  resulting  from  a  synthesis  is  equal  in  weight  to  the  bodies 
synthesised.  That  an  electric  current  resolves  water  into  oxygen  and 
hydrogen  may  be  proved  by  inserting  the  poles  of  a  galvanic  battery  in 
a  vessel  of  water ;  when  this  one  change  is  followed  by  another,  the 
rise  of  babbles  from  each  pole  and  the  very  gradual  decrease  of  the 
water.  If  the  bubbles  are  caught  in  receivers  placed  over  them,  it  can 
be  shown  that  the  joint  weight  of  the  two  bodies  of  gas  thus  formed  is 
equal  to  the  weight  of  the  water  that  has  disappeared ;  and  that  the 


'^4^ 


I 


THE   CANONS   OF   DIRECT   INDUCTION      183 

gases  are  respectively  oxygen  and  hydrogen  may  then  be  shown  by 
proving  that  they  have  the  properties  of  those  gases  according  to 
further  experiments  by  the  Method  of  Difference  ;  as  {e.g.)  that  one  of 
them  is  oxygen,  because  it  supports  combustion,  and  combines  in 
certain  definite  proportions  with  carbon,  sulphur,  etc. 

In  the  more  complex  sciences  the  Method  of  Difference  is  not  so 
generally  applicable,  because  of  the  greater  difficulty  of  being  sure  that 
only  one  circumstance  at  a  time  is  altered  ;  still,  it  is  frequently  used. 
Thus,  if  by  dividing  a  certain  nerve  certain  muscles  are  paralysed,  it  is 
shown  that  normally  that  nerve  controls  those  muscles.  In  his  work 
on  Earth li'oyms,  Darwin  argues  that,  though  sensitive  to  mechanical 
tremors,  they  are  deaf  (or,  at  least,  not  sensitive  to  sonorous  vibrations 
transmitted  through  the  air)  by  the  following  experiment.  He  placed 
a  pot  containing  a  worm  that  had  come  to  the  surface,  as  usual  at  night, 
upon  a  table,  w  hilst  close  by  a  piano  was  violently  played  ;  but  the 
worm  took  no  notice  of  the  noise.  He  then  placed  the  pot  upon  the 
piano  whilst  it  was  being  played,  when  the  worm,  feeling  the  vibrations, 
hastily  slid  back  into  its  burrow. 

When,  instead  of  altering  one  circumstance  in  an  instance  (which  we 
have  done  our  best  not  otherwise  to  disturb)  and  then  watching  what 
follows,  we  try  to  find  ready-made  instances  of  a  phenomenon,  which 
only  differs  in  one  other  circumstance,  it  is,  of  course,  still  more  diffi- 
cult to  be  sure  that  there  is  really  only  one  other  circumstance  in  which 
they  differ.  It  may  be  worth  while,  however,  to  do  our  best  to  find 
such  instances.  Thus,  that  the  temperature  of  ocean  currents  influences 
the  climate  of  the  shores  they  wash,  seems  to  be  shown  by  the  fact  that 
the  average  temperature  of  Newfoundland  is  lower  than  that  of  the 
Norwegian  coast  some  15°  further  north.  Both  regions  have  great  con- 
tinents at  their  back  ;  and  as  the  mountains  of  Norway  are  higher  and 
capped  with  perennial  snow,  we  might  expect  a  colder  climate  there : 
but  the  shore  of  Norway  is  visited  by  the  Gulf  Stream,  whilst  the  shore 
of  Newfoundland  is  traversed  by  a  cold  current  from  Greenland.  Again, 
when  in  1841  the  railway  from  Rouen  to  Paris  was  being  built,  gangs 
of  English  and  gangs  of  French  workmen  were  employed  upon  it,  and 
the  English  got  through  about  one-third  more  work  per  man  than  the 
French.  It  was  suspected  that  this  difference  was  due  to  one  other 
difference,  namely,  that  the  English  fed  better,  preferring  beef  to  thin 
soup.  Now,  logically,  it  might  have  been  objected  that  the  evidence 
was  unsatisfactory,  seeing  that  the  men  differed  in  other  things  besides 
diet — in  '  race '  (say),  which  explains  so  much  and  so  easily.  But  the 
Frenchmen,  having  been  induced  to  try  the  same  diet  as  the  English, 
were,  in  a  few  days,  able  to  do  as  much  work:  so  that  the  "two 
instances"  were  better  than  they  looked.  It  often  happens  that 
evidence,  though  logically  questionable,  is  good  when  used  by  experts, 
whose  familiarity  with  the  subject  makes  it  good. 


i84      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


THE   CANONS   OF   DIRECT   INDUCTION      185 


§  4.  The  Canon  of  Variations. 

Whatever  phenomenon  varies  in  any  manner  wherever  another 

phenomenon  (consequent  or  antecedent)  varies  in  some  particular 

yjianner  [no  other  change  having  concurred]  is  either  a  cause  or 

effect  0/  that phefiome?ion  [or  is  connected  with  it  through  some 

fact  of  causation]. 

This  is  not  an  entirely  fresh  method,  but  may  be  regarded 
as  a  special  case  either  of  Agreement  or  of  Difference,  to  prove 
the  cause  or  effect,  not  of  a  phenomenon  as  a  whole,  but  of 
some  modification  of  it.  There  are  certain  forces,  such  as 
gravitation,  cohesion,  heat,  friction,  that  can  never  be  elimi- 
nated altogether,  and  therefore  can  only  be  studied  in  their 
degrees.  To  such  phenomena  the  method  of  Difference  can 
never  be  fully  applied,  because  there  are  no  negative  instances. 
But  we  may  obtain  negative  instances  of  a  given  quantity  of 
such  a  phenomenon  (say,  heat),  and  may  apply  the  method  of 
Difference  to  that  quantity.  Thus,  if  the  heat  of  a  body  in- 
creases 10  degrees,  from  60  to  70,  the  former  temperature  of 
60  was  a  negative  instance  in  respect  of  those  10  degrees ;  and 
if  only  one  other  circumstance  (say,  friction)  has  altered  at  the 
same  time,  that  circumstance  (if  an  antecedent)  is  the  cause. 
Accordingly,  if  in  the  above  Canon  we  insert,  after  '  particular 
manner  ',  "  [no  other  change  having  concurred]  ",  it  is  a  state- 
ment of  the  method  of  Difference  as  applicable  to  the  in- 
crement of  a  phenomenon  instead  of  to  the  phenomenon  as  a 
whole ;  and  we  may  then  omit  the  last  clause — *'  [or  is  con- 
nected, f/r.]."  For  these  words  are  inserted  to  provide  for  the 
case  of  part-effects  of  a  common  cause  (such  as  the  flash  and 
report  of  a  gun) ;  but  if  no  other  change  (such  as  the  discharge 
of  a  gun)  has  concurred  with  the  variations  of  two  phenomena, 
there  cannot  have  been  a  common  cause,  and  they  are  therefore 
cause  and  effect. 

If,  on  the  other  hand,  we  omit  the  clause  "  [no  other  change' 
having  concurred]  ',  the  Canon  is  a  statement  of  the  method  of 
Agreement  as  applicable  to  the  increment  of  a  phenomenon 


/ 


r 


instead  of  to  the  phenomenon  as  a  whole  ;  and  it  is  then  subject 
to  the  imperfections  of  that  method :  that  is  to  say,  it  leaves 
open  the  possibilities,  that  an  inquirer  may  overlook  a  plurality 
of  causes ;  or  may  mistake  a  connection  of  two  phenomena, 
which  (like  the  flash  and  report  of  a  gun)  are  part-effects  of  a 
common  cause,  for  a  direct  relation  of  cause  and  effect. 

It  may  occur  to  the  reader  that  we  ought  also  to  distinguish  Quali- 
tative and  Quantitative  Variations  as  two  orders  of  phenomena  to  which 
the  present  method  is  applicable.  But,  in  fact,  Qualitative  Variations 
may  be  adequately  dealt  with  by  the  foregoing  methods  of  Agreement, 
Double  Agreement,  and  Diiference ;  because  a  change  of  quality  or 
property  entirely  gets  rid  of  the  former  phase  of  that  quality,  or  substi- 
tutes one  for  another  ;  as  when  the  ptarmigan  changes  from  brown  to 
white  in  winter,  or  as  when  a  stag  sheds  his  antlers.  The  peculiar  use 
of  the  Method  of  Variations,  however,  is  (as  already  observed)  to 
formulate  the  conditions  of  proof  in  respect  of  those  causes  or  effects 
which  cannot  be  entirely  got  rid  of,  but  can  be  obtained  only  in  greater 
or  less  amount ;  and  such  phenomena  are,  of  course,  quantitative. 

We  may  then  illustrate  the  two  cases  of  the  method  thus  : 

Agreement  in  variations — 

ABC  A'  D  E  A'  F  G 

p  q  r  p'    s    t  p"  u   V 

Here  the  accompanying  phenomena  change  from  time  to  time, 
and  the  one  thing  in  which  the  instances  agree  throughout  is 
that  any  increase  of  A  (A'  or  A")  is  followed  or  accompanied 
by  an  increase  of  /  (/'  or  /")  :  whence  it  is  argued  that  A  is 
the  cause  of/,  according  to  Prop.  III.  {a)  (ch.  xv.  §  7).  Still,  it 
is  supposable  that,  in  the  second  instance,  D  or  E  may  be  the 
cause  of  the  increment  of/  ;  and  that,  in  the  third  instance,  F 
or  G  may  be  its  cause.  And,  since  an  actual  investigation  of 
this  type  must  rely  on  observation,  it  is  further  possible  that 
some  undiscovered  cause,  X,  is  the  real  determinant  of  both 
A  and/,  and  of  their  concomitant  variations. 

Professor  Ferri,  in  his  Criminal  Sociology,  observes:  "I  have  shown 
that  in  France  there  is  a  manifest  correspondence  of  increase  and 
decrease  between  the  number  of  homicides,  assaults  and  malicious 
wounding,  and  the  more  or  less  abundant  vintage,  especially  in  the 
years  of  extraordinary  variations,  whether  of  failure  of  the  vintage 


186      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

(1853-5.1859,1867,  1873,  1878-80),  attended  by  a  remarkable  diminu- 
tion of  crime  (assaults  and  wounding),  or  of  abundant  vintages  (1850, 
1856-8,  1862-3,  1865,  1S68,  1874-5),  attended  by  an  increase  of  crime  " 
(p.  117,  Eng.  trans).  And  earlier  he  had  remarked  that  such  crimes 
also  "  in  their  oscillations  from  month  to  month  display  a  characteristic 
increase  during  the  vintage  periods,  from  June  to  December,  notwith- 
standing the  constant  diminution  of  other  ofJ'ences  "  (p.  yj). 

This  is  a  necessary  appeal  to  the  canon  of  Concomitant  Variations, 
because  France  is  never  without  her  annual  vintage,  nor  yet  without 
her  annual  statistics  of  crime.  We  can  only  faintly  imagine  what  would 
happen  if  there  were  no  vintage  !  Still,  it  is  an  argument  whose  cogency 
is  only  that  of  Agreement,  showing  that  very  probably  the  abuse  of  the 
vintage  is  a  cause  of  crimes  of  violence,  but  leaving  open  the  supposi- 
tion, that  some  other  circumstance  or  circumstances,  arising  or  varying 
from  year  to  year,  may  determine  the  increase  or  decrease  of  crime  ; 
or  that  there  is  some  unconsidered  agent  which  afiects  both  the  vintage 
and  crimes  of  violence.  French  sunshine,  it  might  be  urged,  whilst  it 
matures  the  generous  grape,  also  excites  a  morbid  fermentation  in  the 
human  mind. 

Difference  in  Variations  may  be  symbolically  represented 
thus  : 


AB 

A'B 

A '  B 

/^/' 

f  ^I 

Here  the  accompanying  phenomena  are  always  the  same  —  ; 

and  the  only  point  in  which  the  successive  instances  differ  is  in 
the  increments  of  A  (A',  A ")  followed  by  corresponding  incre- 
ments of  /  (/',  / ') :  hence  the  increment  of  A  is  the  cause  of 
the  increment  of/. 

For  examples  of  the  application  of  this  method,  the  reader  should 
refer  to  some  work  of  exact  science.  He  will  find  in  Deschanel's 
Natural  Philosophy,  c.  32,  an  account  of  some  experiments  by  which  the 
connection  between  Heat  and  Mechanical  Work  has  been  established. 
It  is  there  shown  that  "  whenever  work  is  performed  by  the  agency  of 
heat  "  [as  in  driving  an  engine],  "  an  amount  of  heat  disappears  equiva- 
lent to  the  work  performed  ;  and  whenever  mechanical  work  is  spent  in 
generating  heat  "  [as  in  rubbing  two  sticks  together],  "  the  heat  gene- 
rated is  equivalent  to  the  work  thus  spent."  And  an  experiment  of 
Joule's  is  described,  which  consisted  in  fixing  a  rod  with  paddles  in  a 
vessel  of  water,  and  making  it  revolve  and  agitate  the  water  by  means 
of  a  string  wound  round  the  rod,  passed  over  a  pulley  and  attached 
to  a  weight  that  was  allowed  to  fall.     The  descent  of  the  weight  was 


, 


THE   CANONS   OF   DIRECT   INDUCTION      187 

measured  by  a  graduated  rule,  and  the  rise  of  the  water's  temperature 
by  a  thermometer.  "It  was  found  that  the  heat  communicated  to  the 
water  by  the  agitation  amounted  to  one  pound-degree  Fahrenheit  for 
every  772  foot-pounds  of  work  "  expended  by  the  falling  weight.  As  no 
other  material  change  seems  to  take  place  during  such  an  experiment, 
it  shows  that  the  progressive  expenditure  of  mechanical  energy  is  the 
cause  of  the  progressive  heating  of  the  water.  ''"^. 

The  Thermometer  itself  illustrates  this  method.  It  has  been  found  , 
that  the  application  of  heat  to  mercury  expands  it  according  to  a  law  ;  / 
and  hence  the  volume  of  the  mercury,  measured  by  a  graduated  index,  is 
used  to  indicate  the  temperature  of  the  air,  water,  animal  body,  etc.,  in 
which  the  thermometer  is  immersed,  or  with  which  it  is  brought  in 
contact.  In  such  cases,  if  no  other  change  has  taken  place,  the  heat  of 
the  air,  water,  or  body,  is  the  cause  of  the  rise  of  the  mercury  in  its 
tube.  If  some  other  substance  (say  spirit)  be  substituted  for  mercury 
in  constructing  a  thermometer,  it  serves  the  same  purpose,  provided  the 
index  be  graduated  according  to  the  law  of  the  expansion  of  that  sub- 
stance by  heat,  as  experimentally  determined. 

It  may  be  added  that  instances  of  phenomena  that  do  not  vary 
together  indicate  the  exclusion  of  a  supposed  cause  (by  Prop.  III.  (r)). 

The  I^Graphic  JNIethod  is  an  interesting  way  of  exhibiting 
Concomitant  Variations  to  the  eye.  It  is  extensively  used  in 
physical  and  statistical  inquiries.  Along  a  horizontal  line  (the 
abscissa)  is  measured  one  of  the  conditions  (or  agents)  with 
which  the  inquiry  is  concerned,  called  the  Variable  ;  and  along 
perpendiculars  (ordinates)  is  measured  some  phenomenon  to  be 
compared  with  it,  called  the  Variant. 

Thus,  the  expansion  of  a  liquid  by  heat  may  be  represented  by 
measuring  degrees   of   temperature   along  the  horizontal,  and  the  ex- 


FiG.  9. 


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De^jrees  of  Htuit 


pansion   of  a    column    of    the    liquid    in    units    of   length   along   the 
perpendicular. 
In   the  next    Diagram,    reduced    from    one   given    by    Mr.    C.    H. 


i88      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


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THE   CANONS   OF   DIRECT   INDUCTION     189 

Denyer  in  an  article  on  the  price  of  tea  {Economic  Journal,  No.  9),  the 
condition  measured  horizontally  is  Time  ;  and,  vertically,  three  variants 
are  measured  simultaneously,  so  that  their  relations  to  one  another 
from  time  to  time  may  be  seen  at  a  glance. 

From  this  it  is  evident  that,  as  the  Duty  on  Tea  falls,  the  Price  of 
Tea  falls,  whilst  the  Consumption  of  Tea  rises ;  and,  in  spite  of  some 
irregularity  of  correspondence  in  the  courses  of  the  three  phenomena, 
their  general  causal  connection  can  hardly  be  mistaken. 

It  will  be  noticed  that  these  three  lines,  especially  those  of  Price  and 
Consumption  (which  may  be  considered  natural  resultants,  in  contrast 
with  the  arbitrary  fixation  of  a  Tax),  do  not  depart  widely  from  regular 
curves ;  and  accordingly,  assuming  the  causes  at  M^ork  to  vary  con- 
tinuously during  the  intervals  between  points  of  measurement,  curves 
may  be  substituted.  In  fact,  a  curve  often  represents  the  course  of  a 
phenomenon  more  truthfully  than  can  be  done  by  a  line  that  zigzags 
along  the  exact  measurements ;  because  it  is  less  influenced  by  tem- 
porary and  extraordinary  causes  that  may  obscure  the  operation  of 
those  that  are  being  investigated.  On  the  other  hand,  the  abrupt 
deviations  of  a  punctilious  zigzag  may  have  their  own  logical  value,  as 
will  appear  in  the  next  section. 


§  5.  The  Canon  of  Residues. 

Subduct  from  any  phe?iomenon  such  part  as  previous  induc- 
tions have  shown  to  be  the  effect  of  certain  antecedents,  and  the 
residue  of  the  phenomeno7i  is  the  effect  of  the  reinai?iing  ante- 
cedents. 

The  phenomenon  is  here  assumed  to  be  an  effect :  a  similar 
Canon  may  be  framed  for  residuary  causes. 

This  also  is  not  a  fresh  method,  but  a  special  case  of  the 
method  of  Difference.  For  if  we  suppose  the  phenomenon  to 
hep  q  r,  and  the  antecedent  to  be  A  B  C,  and  that  we  already 
know  B  and  C  to  have  (either  severally  or  together)  the  con- 
sequents g  r,  in  which  their  efificacy  is  exhausted  ;  we  may 

B  C 

regard as  an  instance  of  the  absence  of  /  obtained  deduc- 

q  r 

ABC 
tively  from  the  whole  phenomenon by  our  knowledge  of 

P  q  r     ' 

ABC 

the  laws  of  B  and  C ;  so  that —  is  an  instance  of  the 

P  V  ^ 


I90      LOGIC:    DEDUCTIVE    AND   INDUCTIVE 
presence  of/,  differing  otherwise  from  ^-^  in  nothing  except 

^  r  or 

that  A  is  also  present.  By  the  Canon  of  Difference,  therefore 
A  is  the  cause  of  /.  Or,  again,  when  phenomena  thus  treated 
are  strictly  quantitative,  the  method  may  be  based  on  Prop. 
III.  (/O,  ch.  XV.  §  7. 

Of  course,  if  A  can  be  obtained  apart  from  B  C  and  directly 
experimented  with  so  as  to  produce/,  so  much  the  better;  and 
this  may  often  be  done  ;  but  the  special  value  of  the  method 
of  Residues  appears,  when  some  complex  phenomenon  has  been 
for  the  most  part  accounted  for  by  known  causes,  whilst  there 
remains  some  excess,  or  shortcoming,  or  deviation  from  the 
result  which  those  causes  alone  would  lead  us  to  expect,  and 
this  residuary  fact  has  to  be  explained  in  relation  to  the  whole. 
Here  the  negative  instance  is  constituted  by  deduction,  showing 
what  would  happen  but  for  the  interference  of  some  unknown 
cause  which  is  to  be  investigated ;  and  this  prominence  of  the 
deductive  process  has  led  some  writers  to  class  the  method  as 
deductive.  But  we  have  seen  that  all  the  Canons  involve 
deduction ;  and,  considering  how  much  in  every  experiment  is 
assumed  as  already  known  (what  circumstances  are  *  material,' 
and  when  conditions  may  be  called  '  the  same  '),  the  wonder 
is  that  no  one  has  insisted  upon  regarding  every  method  as 
concerned  with  residues.  In  fact,  as  scientific  explanation 
progresses,  the  phenomena  that  may  be  considered  as  residuary 
become  more  numerous  and  the  importance  of  this  method 
increases. 

Examples  :  The  recorded  dates  of  ancient  eclipses  having  been  found 
to  differ  from  those  assigned  by  calculation,  it  has  been  surmised  that 
the  average  length  of  a  day  may  in  the  meanwhile  have  increased.  If 
so,  this  is  a  residuary  phenomenon  not  accounted  for  by  the  causes 
formerly  recognised  as  determining  the  rotation  of  the  earth  on  its 
axis ;  and  it  may  be  explained  by  the  doctrine  that  the  tides,  by  their 
friction,  are  reducing  the  rate  of  the  earth's  rotation,  and  thereby 
lengthening  the  day. 

Capillarity  seems  to  be  a  striking  exception  to  the  principle  that 
water  (or  any  liquid)  '  finds  its  level,'  that  being  the  condition  of  equili- 
brium; yet  capillarity  proves  to  be  only  a  refined  case  of  equilibrium 


THE   CANONS   OF   DIRECT   INDUCTION      191 


when  account  is  taken  of  the  forces  of  adhesion  generated  by  different 
kinds  of  bodies  in  contact. 

"  Many  of  the  new  elements  of  Chemistry,"  says  Herschel,  "have 
been  detected  in  the  investigation  of  residual  phenomena."  Thus, 
Lord  Rayleigh  found  that  nitrogen  from  the  atmosphere  was  slightly 
heavier  than  nitrogen  got  from  chemical  sources.  The  search  for  the 
cause  of  this  difference  led  to  the  discovery  of  argon. 

Darwin  suggested  Sexual  Selection  as  a  means  of  explaining  certain 
modifications  of  animals  in  form,  colouration,  or  habits,  which  did  not 
seem  to  him  to  have  resulted  from  their  struggle  for  existence  in  relation 
to  other  species  or  to  external  conditions. 

The  economist  shows  that  when  a  country  imports  goods  the  chief 
means  of  paying  for  them  is  to  export  other  goods.  If  this  were  all, 
imports  and  exports  would  be  of  equal  value  :  but  the  United  Kingdom 
imports  about  /40o,ooo,ooo  annually,  and  exports  about  ;^3oo,ooo,ooo. 
Here,  then,  is  a  residuary  phenomenon  of  ;^  100,000,000  to  be  accounted 
for.  But  foreign  countries  owe  us  about  ;^5o,ooo,ooo  for  the  use  of 
shipping,  and  £70,000,000  as  interest  on  the  capital  we  have  lent  them, 
and  ;^ 1 5. 000, 000  in  commissions  upon  business  transacted  for  them. 
These  sums  added  together  amount  to  ;^ 1 35,000,000 ;  and  that  is 
;^35, 000,000  too  much.  Thus  another  residuary  phenomenon  emerges  ; 
for  whilst  foreigners  seem  to  owe  us  ;^435,ooo,ooo,  they  only  send  us 
;^40o,ooo,ooo  of  imports.  To  account  for  these  ;^35,ooo,ooo,  we  may 
suppose  that  they  represent  the  annual  investment  of  our  capital 
abroad,  in  return  for  which  no  immediate  payment  is  due  ;  and,  these 
being  omitted,  exports  and  imports  balance. 

When,  in  pursuing  the  method  of  Variations,  the  phenomena  com- 
pared do  not  always  correspond  in  their  fluctuations,  the  irregular 
movements  of  that  phenomenon  which  we  regard  as  the  effect  may 
often  be  explained  by  treating  them  as  residuary  phenomena,  and  then 
seeking  for  exceptional  causes,  whose  temporary  interference  has  ob- 
scured the  influence  of  the  general  cause.  Thus,  returning  to  the  dia- 
gram of  the  Price  of  Tea  in  §  4,  it  is  clear  that  generally  the  Price  falls 
as  the  Duty  falls;  but  in  Mr.  Denyer's  more  minutely  wrought  diagram, 
from  which  this  is  reduced,  it  may  be  seen  that  in  1840  the  Price  of  Tea 
rose  from  3s.  gd.  to  4s.  gd.  without  any  increase  of  Duty.  This,  how- 
ever, is  readily  explained  by  the  Chinese  War  of  that  year,  which,  of 
course,  checked  the  trade.  Again,  from  1869  to  1889  the  Duty  was 
constant,  whilst  the  Price  of  Tea  fell  as  much  as  8^.  per  lb. ;  but  this 
residuary  phenomenon  is  explained  by  the  prodigiously  increased  pro- 
duction of  Tea  during  that  period  in  India  and  Ceylon. 


CHAPTER   XVII 


COMBINATION   OF   INDUCTION   WITH   DEDUCTION 


§  I.  We  have  now  reviewed  Mill's  five  Canons  of  Inductive 
Proof.  At  bottom,  as  he  observes,  there  are  only  two,  namely. 
Agreement  and  Difference ;  since  the  Double  Method,  Varia- 
tions and  Residues  are  (as  we  have  seen)  only  special  forms  of 
the  other  two.  And  indeed  it  may  almost  be  said  that  in  the 
final  analysis  they  are  all  reducible  to  one,  namely,  Difference ; 
for  the  cogency  of  the  Method  of  Agreement,  as  distinguished 
from  a  simple  enumeration  of  instances  agreeing  in  the 
coincidence  of  a  supposed  Cause  and  its  Effect,  depends 
upon  the  omission,  in  one  instance  after  another,  of  all  other 
circumstances;  which  omission  is  a  point  of  difference. 

Now,  the  Canons  are  an  analysis  of  the  conditions  of 
proving  directly,  by  means  of  observation  or  experiment,  any 
proposition  that  predicates  causation.  Rut  if  we  say  '  by 
means  of  observation  or  exoeriment,'  it  is  not  to  be  under- 

A.  ' 

stood  that  these  are  the  only  means  and  that  nothing  else  is 
involved ;  for  it  has  been  shown  that  the  Law  of  Causation 
is  itself  an  indispensable  foundation  of  the  evidence.  In  fact 
Inductive  Logic  may  be  considered  as  having  a  purely 
formal  character.  It  consists,  first,  in  a  statement  of  the 
Law  of  Cause  and  Effect ;  secondly,  in  certain  immediate 
inferences  from  this  Law,  expanded  into  the  Canons  ;  thirdly, 
in  the  syllogistic  application  of  the  Canons  to  special  proposi- 
tions of  causation  by  means  of  minor  premises,  showing  that 
certain  instances  satisfy  the  Canons. 


COMBINED  INDUCTION  AND  DEDUCTION     193 

At  the  risk  of  some  pedantry,  we  may  exhibit  the  process  as 
follows  (cf.  Prof.  Ray's  Logic :  Appendix  D)  : 

Whatever  relation  of  events  has  certain  marks  is  a  case  of 
Causation ; 

The  relation  A :  /J  has  some  or  all  of  these  marks  (as  shown 
by  observation  and  by  the  conformity  of  instances  to 
such  or  such  a  Canon)  : 
Therefore,  the  relation  A  :  /  is  a  case  of  Causation. 
Now,  the  parenthesis,  "as  shown  by  the  conformity,  eU.,"  is  an 
adscititious  member  of  an  Epicheirema,  which  may  be  stated,  as 
a  Prosyllogism,  thus : 

If  an  instance,  etc.  (Canon  of  Difference) ; 

A  B  C     BC 

are  of  the  kind  required  : 


The  instances 


P  q  r      q  r 

Therefore,  the  antecedent  A,   present  where  /  occurs  and 
absent  where  it  does  not  occur,  is  the  cause  of/. 

Such  is  the  bare  Logic  of  Induction:  so  that,  strictly 
speakmg,  observation  or  experiment  is  no  part  of  the  logic, 
but  a  means  of  applying  the  logic  to  actual,  that  is,  not  merely 
symbolical,  propositions.  The  Formal  Logic  of  Induction  is 
essentially  deductive;  and  it  has  been  much  questioned 
whether  any  transition  from  the  formal  to  the  material 
conditions  of  proof  is  possible.  As  long  as  we  are  content 
to  illustrate  the  Canons  with  symbols,  such  as  A  and  /,  all 
goes  well ;  but  can  we  in  any  actual  investigation  show  that  the 
relevant  facts  or  '  instances  '  correspond  with  those  symbols  ? 

In  the  first  place,  as  Dr.  Venn  shows,  natural  phenomena 
want  the  distinctness  and  capability  of  isolation  that  belong 
to  symbols.  Secondly,  the  observing  whether  instances  conform 
to  a  Canon,  must  always  be  subject  at  last  to  the  limits  of  our 
faculties.  How  can  we  ascertain  exact  equality,  immediate 
sequence?  The  Canon  of  Difference,  in  its  experimental 
application,  is  usually  considered  the  most  cogent  sort  of 
proof:  yet  when  can  the  two  sequent  instances,  before  and 
after  the  introduction  of  a  certain  agent,  be  said  to  differ  in 
nothing  else  ?     Are  not  earth  and  stars  always  changing  posi- 

N 


194      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

tion ;  is  not  every  molecule  in  the  room  and  apparatus  always 
oscillating?  It  is  true  that  our  senses  are  now  aided  by 
elaborate  instruments ;  but  the  construction  of  these  depends 
on  scientific  theories,  which  again  depend  on  experiments. 

It  is  right  to  touch  upon  this  well-known  sceptical  topic ; 
but  to  insL  much  upon  it  is  not  a  sign  of  good  sense.  The 
works  of  Herschel,  Whewell,  and  Jevons  should  be  consulted 
for  the  various  methods  of  correcting  observations,  by  repeating 
them,  averaging  them,  verifying  one  experimental  process  by 
another,  always  refining  the  methods  of  exact  measurement, 
multiplying  the  opportunities  of  error  (that  if  any  exist  it  may 
at  last  show  itself),  and  by  other  devices  of  what  may  be  called 
Material  Logic.  But,  probably,  only  many  years  spent  in  the 
study  and  personal  manipulation  of  scientific  processes,  can 
give  a  just  sense  of  their  effectiveness ;  and  to  stand  by,  sug- 
gesting academic  doubts,  is  easier  and  more  amusing. 

§  2.  Still,  it  is  not  so  much  in  laws  based  upon  direct  obser- 
vation or  experiment,  that  the  material  validity  of  scientific 
reasoning  appears,  as  in  the  cumulative  evidence  that  arises 
from  the  co-ordination  of  laws  within  each  science,  and  the 
growing  harmony  and  coherence  of  all  sciences.    This  requires 
a  more  elaborate  combination  of  deduction  with  observation 
and  experiment.     During  the  last  three  hundred  years  many 
departments  of  science  have  been  reduced  under  prmciples  of 
the  greatest  generality,  such  as  the  Law  of  Gravitation,  the 
Undulatory  theory  of  Light,  the  Conservation  of  Energy,  and 
the  Theory  of  Natural  Selection ;  connecting  and  explaining 
the  less  general  laws,  which,  again,  are  said  to  connect  and 
explain  the  facts.     Meanwhile,  those  sciences  that  were  the 
first  to  make  progress  have  been  useful  in  developing  others 
which,  like  Biology  and  Sociology,  present  greater  difticulties. 
In   fact  it  is  more  and  more  apparent  that  the   distinctions 
drawn   among  Sciences  are   entirely   for  the  convenience  of 
study  and  that  all  Sciences  tend  to  merge  in  one  universal 
Science  of  Nature.     Now,  this  process  of  the  '  unification  of 
knowledge '  is  almost  another  name  for  deduction  ;  but  at  the 


COMBINED  INDUCTION  AND  DEDUCTION     195 

same  time  it  depends  for  its  reality  and  solidity  upon  a 
constant  reference  to  observation  and  experiment.  Of  the 
logical  character  of  this  process  only  a  very  inadequate  notion 
can  be  given  in  the  ensuing  chapters. 

Let  us  begin  by  returning  to  some  earlier  considerations. 
We  have  seen  in  chap.  xiv.  §  6,  that  when  two  or  more  agents 
or  forces  combine  to  produce  a  phenomenon,  their  effects  are 
intermixed  in  it,  and  this  in  two  ways  according  to  their  nature. 
In  chemical  action  and  in  vegetable  and  animal  life,  the  causes 
concerned  are  blended  in  their  results  in  such  a  way  that  most 
of  the  qualities  which  they  exhibited  severally  are  lost,  whilst 
new  qualities  appear  instead.  Thus  chlorine  (a  gas)  and 
sodium  (a  metal),  in  a  certain  combination,  form  common  salt; 
which  is  quite  unlike  either  of  them  :  a  man  eats  bread,  and  it 
becomes  muscle,  nerve  and  bone.  In  such  cases  we  cannot 
trace  the  qualities  of  the  causes  in  the  qualities  of  the  effects ; 
given  such  causes,  we  can  prove  by  experimental  analysis  and 
synthesis,  according  to  the  canons  of  induction,  that  they  have 
such  effects ;  but  we  may  not  be  able  in  any  new  case  to  calcu- 
late what  the  effects  will  be. 

On  the  other  hand,  in  Astronomy  and  Physics,  the  causes 
treated  of  are  mechanical ;  at  least,  it  is  the  aim  of  Physics  to 
attain  to  a  mechanical  conception  of  phenomena ;  so  that,  in 
every  new  combination  of  forces,  the  intermixed  effect,  or  re- 
sultant, can  be  calculated  beforehand ;  provided  that  the  forces 
concerned  admit  of  being  quantitatively  estimated,  and  that 
the  conditions  of  their  combination  are  not  so  complex  as  to 
baffle  the  powers  of  mathematicians.     In  such  cases,  therefore, 
when  direct  observation  or  experiment  is  insufficient  to  resolve 
an  effect  into  the  laws  of  its  causes,  the  general  method  is   to     ) 
calculate  what  may  be  expected  from  a  combination   of  its     r 
causes,  either  as  known  or  hypothetically  assumed,   and   to     ! 
compare  the  anticipation  with  the  actual  phenomenon.  J 

§  3.  This  is  what  Mill  calls  the  Direct  Deductive  Method; 
or,  the  Physical  Method,  because  it  is  so  much  relied  on  in 
treating  of  Light,   Heat,  Sound,  etc.\   though  it  is  also  the 


196      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 
usual   method   of    Astronomy   and    Economics;    Deduction 
leads  the  way,  and  its  results  are  tested  by  f  "<=''-  3", 
ments    or    observations.     Given    any    complex    mechanical 
phenomenon,  the  inquirer  considers-(.)  what  laws  already 
ascertained  by  induction  seem  likely  to  apply  to  .t  (m  default 
of  known  laws,  hypotheses  are  substituted  :  cf.  chap,  xvni.) ;  he 
then"  (.)  computes  the  effect  that  will  follow  from  these  laws 
in  circumstances  similar  to  the  case  before  him  ;  and  (3)  be 
verifies  his  conclusion  by  comparing  it  with  the  actual  pheno- 
menon. 

A  ^ell-tried  and  staunch  example  of  this  method  is  the  explanation 
of  the  rise  of  .ater  in  the  •common  pump.'     We  know  three  law 
aii^' able  to  this  case:  ,.)  that  the  a.-sphere  weighs  upon  the  wte 
outside  the  pump  with  a  pressure  of  14  lb.  to  the  square  inch     (i-   tha 
a  iTquid  (and  therefore   the  water)   transmits   pressure   equally    n  al 
di    cUon    (upwards  as  svell  as  downwards  and  sideways)     and  (.)  that 
nressure  upon  a  body  in  any  direction,  if  not  counteracted  by  an  oppo- 
site pressure,  produces  motion.     Hence,  when  the  rise  of  the  p.stott  of 
he  pump  r  moves  the  pressure  upon  the  water  withm  the  cy  mder 
tending  to  produce  a  vacuum  there,   this  water  is  pushed  up  by    he 
pres  ure  of^the  air  upon  the  water  outside  the  cylinder,  and  follows  the 
risfnepiston,  until  L  column  of  water  inside  the  cylinder  exerts  a 
pressure  equkl  to  that  of  the  atmosphere  upon  a  given  area.     So  much 
?or  the  computation  ;  does  it  correspond  with  the  fact  ?    It  ,s  found  tha 
at  the  sea-level  water  can  be  pumped  to  the  height  of  32  feet    and  that 
such  a  column  of  water  has  a  pressure  of  .4  lb.  to  the  square  inch.   We 
™^v  show  further  that,  at  the  sea  level,  spirits  of  wine  may  be  pumped 
r.Lr  a  corig  to  it^  less  speciBc  gravity ;  and  that  if  we  attempt  to 
pump  water  at  successive  altitudes  above  the  sea  level,  we  can  only  raise 
Ft  t^Us  and  less  heights,  corresponding  with  the  lessened  atmospheric 
prrssure  at  those  aUitudes,   where  the  column  of  air  producing  the 
^esu  e  is  shorter.     Finally,  if  we  try  to  work  a  pump,  having  first  pro- 
duced  a  vacuum  over  the  water  outside  the  cylinder,  we  shall  find  that 
the  water  inside  will  not  rise  at  all;  the  piston  can  be  raised,  but  the 
watr  does  not  follow  it.    The  verification  thus  shows  that  the  com- 
puted effect  corresponds  with  the  phenomenon  to  be  explained    that 
Ihe  result  does  not  depend  upon  the  nature  of  water  only,  bu'    s  '  "e 
(allowing  for  differences  of  specific  gravity)  of  other  liquids ,  that  if  the 
pressure  of  the  outside  air  is  diminished,  the  height  of  pumping  is  so 
wo  (canon  of  Variations) ;  and  that  it  that  pressure  is  entirely  removed, 
Dumping  becomes  impossible  (canon  of  Difference). 

Any  text-book  of  Astronomy  or  Physics  furnishes  numerous  lUustra- 


i 


COMBINED  INDUCTION  AND  DEDUCTION     197 

tions  of  this  method.  Take,  for  example,  the  first  chapter  of  Deschanel's 
Optics,  where  are  given  three  methods  of  determining  the  velocity  of 
Light.  This  was  first  deduced  from  observation  of  Jupiter's  satellites. 
The  one  nearest  the  planet  passes  behind  it,  or  into  its  shadow,  and  is 
eclipsed  at  intervals  of  about  42^  hours.  But  it  can  be  shown  that, 
when  Jupiter  and  the  Earth  are  nearest  together  on  the  same  side  of 
the  Sun,  an  eclipse  of  this  satellite  is  visible  from  the  earth  16  min. 
266  sec.  earlier  than  when  Jupiter  and  the  Earth  are  furthest  apart  on 
opposite  sides  of  the  Sun :  16  min.  26' 6  sec,  then,  is  the  time  in  which 
light  traverses  the  diameter  of  the  Earth's  orbit.  Therefore,  supposing 
the  Earth's  distance  from  the  Sun  to  be  91^  millions  of  miles,  light 
travels  about  185,500  miles  a  second.  Another  deduction,  agreeing 
with  this,  starts  from  the  fact  of  aberration,  or  the  displacement  of  the 
apparent  from  the  actual  position  of  the  stars  in  the  direction  of  the 
earth's  motion.  Aberration  depends  partly  on  the  velocity  of  light, 
partly  on  the  velocity  of  the  Earth ;  and  the  latter  being  known,  the 
former  can  be  computed.  Now,  these  two  deductive  arguments,  verify- 
ing each  other,  have  also  been  verified  experimentally.  Foucault's 
experiment  to  measure  the  velocity  of  light  is  too  elaborate  to  be 
described  here :  a  full  account  of  it  will  be  found  in  the  treatise  above 
cited,  §  687. 

When  the  phenomena  to  be  explained  are  of  such  a  character,  so  vast 
in  extent,  power  or  duration,  that  it  is  impossible,  in  the  actual  circum- 
stances of  the  case,  to  frame  experiments  in  order  to  verify  a  deductive 
explanation,  it  may  still  be  possible  to  reproduce  a  similar  phenomenon 
upon  a  smaller  scale.     Thus  Monge's  explanation  of  mirage  by  the 
great  heat  of  the  desert  sand,  which  makes  the  lowest  stratum  of  air 
less  dense  than  those  above  it,  so  that  rays  of  light  from  distant  objects 
are  refracted  in  descending,   until  they  are  actually  turned  upwards 
again  to  the  eye  of  the  beholder,  giving  him  inverted  images  of  the 
objects  as  if  they  were  reflected  in  water,   is  manifestly  incapable  of 
being  verified  by  experiment  in  the  natural  conditions  of  the  pheno- 
menon.    But  by  heating  the  bottom  of  "  a  sheet-iron  box,  with  its  ends 
cut  away,"  the  rarefied  air  at  the  bottom  of  the  box  may  sometimes  be 
made  to  yield  reflections  ;  and  this  shows  at  least  that  the  supposed 
cause  is  a  possible  one  (Deschanel,  Optics,  §  726).     Similarly  as  to  the 
vastest  of  all  phenomena,  the  evolution  of  the  stellar  system,  and  of  the 
solar  system  as  part  of  it,  from  an  immense  cloudlike  volume  of  matter : 
Mr.  Spencer,  in  his  Essay  on  The  Nebular  Hypothesis  {Essays,  I.  vi.),  says, 
amidst  a  great  array  of  deductive  arguments  from  mechanical  principles, 
that  "  this  ci  priori  reasoning  harmonises  with  the  results  of  experiment. 
Dr.  Plateau  has  shown  that  when  a  mass  of  fluid  is,  as  far  as  may  be, 
protected  from  the  action  of  external   forces,  it  will,  if  made  to  rotate 
with  adequate  velocity,  form  detached  rings ;  and  that  these  rings  will 
break  up  into  spheroids,  which  turn  on  their  axes  in  the  same  direction 


198      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

Nvith  the  central  mass."     The  theory  of  the   evolution  of  species   of 
plants  and  animals  by  Natural   Selection,  again,  though,  of  course,  it 
cannot  be  verified  by  direct  experiment  (since  experiment  implies  arti- 
ficial arrangement),  and  the  process  is  too  slow  for   observation,  is 
nevertheless,  to  some  extent  confirmed  by  the  practice  of  gardeners  and 
breeders  of  animals.     Since,  by  taking  advantage  of  accidental  varia- 
tions of  form  and  colour  in  the  plants  or  animals  under  their  care,  and 
relying  on  the  heritability  of  these  variations,   they  obtain  extensive 
modifications  of  the  original  stocks,   and  adapt  them  to  the  various 
purposes  for  which  flowers  and  cereals,  poultry,  dogs  and  cattle  are 
domesticated.     This  shows,  at  least,  that  living  forms  are  plastic  and 
extensively  modifiable  in  a  comparatively  short  time. 

§  4.  Suppose,  however,  that,  in  verifying  a  deductive  argu- 
ment, the  effect  as  computed   from  the  laws  of  the  causes 
assigned,  does  not  correspond  with  the  facts  observed  :  there 
must  then    be   an   error    somewhere.     If  the    fact  has  been 
accurately  observed,  the  error  must  he  cither  in  the  process  of 
deduction  and  computation,  or  else  in  the  premises.     As  to 
the  process  of  deduction,  it  may  be  very  simple  and  easily 
revised,  as  in  the  above  explanation  of  the  common  pump ; 
or  it  may  be  very  involved  and  comprise  long  trains  of  mathe- 
matical calculation.     If,  however,  on  re-examining  the  compu- 
tations, we  find  them  correct,  it  remains  to  look  for   some 
mistake  in  the  premises. 

(I)  We  may  not  have  accurately  ascertained  the  laws,  or  the  modes 
of  operation,  of  the  forces  present.  Thus,  the  rate  at  which  bodies  fall 
was  formerly  believed  to  vary  in  proportion  to  their  relative  weights  ; 
and  any  estimate  based  upon  this  belief  is  not  likely  to  have  agreed 
with  the  facts.  Again,  the  corpuscular  theory  of  light,  namely,  that 
the  physical  cause  of  light  is  a  stream  of  fine  particles  projected  in 
straight  lines  from  the  luminous  object,  though  it  seemed  adequate  to 
the  explanation  of  many  optical  phenomena,  could  not  be  made  to 
agree  with  the  facts  of  interference  and  double  refraction. 

(2)  The  circumstances  in  which  the  agents  are  combined  may  not 
have  been  correctly  conceived.  When  Newton  began  to  inquire  whether 
the  attraction  of  the  earth  determined  the  orbit  of  the  moon,  he  was  at 
first  disappointed.  "  According  to  Newton's  calculations,  made  at  this 
time  "  says  Whewell.  "  the  moon,  by  her  motion  in  her  orbit,  was 
deflected  from  the  tangent  every  minute  through  a  space  of  thirteen  feet. 
But  by  noticing  the  space  which  bodies  would  fall  in  one  minute  at  the 
earth's  surface,  and  supposing  this  to  be  diminished  in  the  ratio  of  the 


COMBINED  INDUCTION  AND  DEDUCTION     199 

inverse  square,  it  appeared  that  gravity  would,  at  the  moon's  orbit, 
draw  a  body  through  more  than  fifteen  feet."  In  view  of  this  discre- 
pancy he  gave  up  the  inquiry  for  sixteen  years,  until  in  1682,  having 
obtained  better  data,  he  successfully  renewed  it.  "  He  had  been  mis- 
taken in  the  magnitude  of  the  earth,  and  consequently  in  the  distance 
of  the  moon,  which  is  determined  by  measurements  of  which  the  earth's 
radius  is  the  base."  It  was  not,  therefore,  a  mistake  as  to  the  law  or 
nature  of  the  forces  concerned  (namely,  the  law  of  the  inverse  square 
and  the  identity  of  celestial  with  terrestrial  gravity),  but  as  to  the  cir- 
cumstances in  which  the  agents  (earth  and  moon)  were  combined,  that 
prevented  his  calculations  being  verified.     {Hist.  Ind.  Sc. :  VII.  ii.  3.) 

(3)  One  or  more  of  the  agents  affecting  the  result  may  have  been 
overlooked  and  omitted  from  the  estimate.   Thus,  an  attempt  to  explain 
the  tides  by  taking  account  only  of  the  earth  and  the  moon  will  not 
entirely  agree  with  the   facts,  since  the  sun  also  influences  the  tides. 
This  illustration,  however,  shows  that  when  the  conclusion  of  a  deduc- 
tive explanation  does  not  entirely  agree  with  the  facts,  it  is  not  always 
to  be  inferred  that  the  reasoning  is,  properly  speaking,  wrong  ;  it  may 
be  right  as  far  as  it  goes,  and  merely  inadequate.     Hence  (a)  it  is  often 
in  just  such  cases  that  an  opportunity  occurs  of  applying  the  Method  of 
Residues,  by  discovering  the  agent  that  must  be  allowed  for  in  order  to 
complete  the  explanation.     And  {b)  the  investigation  of  a  phenomenon 
is  often  designedly  begun  upon  an  imperfect  basis  for  the  sake  of  sim- 
plicity ;    the  result  being  regarded  as    a   first   approximation,   to  be 
afterwards  corrected  by  including  one  by  one  the  remaining  agents  or 
circumstances  affecting  the  phenomenon,  until  the  theory  is  complete ; 
that  is.  until  its  agreement  with  the  facts  is  satisfactory. 

(4)  We  may  have  included  among  the  data  of  our  reasonings  agents 
or  circumstances  that  do  not  exist  or  do  not  affect  the  phenomenon  in 
question.     In  the  early  days  of  science  purely  fanciful  powers  were 
much  relied  upon :  such  as  the  solid  spheres  that  carried  the  planets 
and  stars ;  the  influence  of  the  planets  upon  human  destiny ;  the  ten- 
dency of  everything  to  seek  "  its  own  place,"  so  that  fire  rises  to  heaven, 
and  solids  fall  to  the  earth ;  the  "  plastic  virtue  "  of  the  soil,  which  was 
once  thought  to  have  produced  fossils.     It  may  be  said,  however,  that 
when  such  conceptions  hindered  the  progress  of  explanation,  it  was  not 
so  much  by  vitiating  the  deductive  method  as  by  putting  men  off  from 
exact  inquiries.     More  to  our  present  purpose  were  the  supposed  cata- 
clysms, or  extraordinary  convulsions  of  the  earth,  a  belief  in  which 
long  hindered  the  progress  of  Geology.     Again,  in  Biology.  Psychology, 
and   Sociology   many   explanations  have  depended  upon  the   doctrine 
that  any  improvement  of  structure  or  faculty  acquired  by  an  individual 
may  be  inherited  by  his  descendants :  as  that,  if  an  animal  learns  to 
climb  trees,  his  offspring  have  a  greater  aptitude  for  that  mode  of  life  ; 
that  if  a  man  tries  to  be  good,  his  children  find  it  easier  to  be  virtuous  ; 


200 


LOGIC:   DEDUCTIVE   AND   INDUCTIVE 


that  if  the  inhabitants  of  a  district  carry  on  cloth-work,  it  becomes 
easier  for  each  successive  generation  to  acquire  dexterity  in  that  art. 
But  now  the  heritabiUty  of  powers  acquired  by  the  individual  through 
his  own  efforts,  is  disputed  ;  and,  if  the  denial  be  made  good,  all  such 
explanations  as  the  above  must  be  revised. 

Clearly,  then,  if  the  premises  of  a  deductive  argument  be  vitiated  in 
any  of  these  four  ways,  its  conclusion  will  fail  to  agree  with  the  results 
of  observation  and  experiment,  unless,  of  course,  one  kind  of  error 
happen  to  be  cancelled  by  another  that  is  '  equal  and  opposite.'  We 
now  come  to  a  variation  of  the  method  of  combining  Induction  with 
Deduction,  so  important  as  to  require  separate  treatment. 

§  5.  The  Inverse  or  Historical  Method  has  of  late  years 
become  remarkably  fruitful.  When  the  forces  determining  a 
phenomenon  are  too  numerous,  or  too  indefinite,  to  be  com- 
bined in  a  direct  deduction,  we  may  begin  by  collecting  an 
empirical  law  of  the  phenomenon  (as  that  '  the  democracies  of 
City-states  are  arbitrary  and  fickle'),  and  then  endeavour  to 
show  by  deductions  from  "  the  nature  of  the  case,"  that  is, 
from  a  consideration  of  the  circumstances  and  forces  known 
to  be  operative  (of  which,  in  the  above  instance,  the  most 
important  is  sympathetic  contagion),  that  such  a  law  was  to 
be  expected.  Deduction  is  thus  called  in  to  verify  a  previous 
Induction;  whereas  in  the  'Physical  Method'  a  Deduction 
was  verified  by  comparing  it  with  an  Induction  or  an  experi- 
ment; hence  the  Method  now  to  be  discussed  has  been  named 
the  Inverse  Deductive  Method. 

But  although  it  is  true  that,  in  such  inquiries  as  we  are  now 
dealing  with,  Induction  generally  takes  the  lead ;  yet  I  cannot 
think  that  the  mere  order  in  which  the  two  logical  processes 
occur  is  the  essential  distinction  between  the  two  ways  of 
combining  them.  For,  in  the  first  place,  in  investigations  of 
any  complexity  both  Induction  and  Deduction  recur  again 
and  again  in  whatever  order  may  be  most  convenient ;  and,  in 
the  second  place,  the  so-called  'inverse  order'  is  sometimes 
resorted  to  in  Astronomy  and  Physics.  For  example,  Kepler's 
Laws  were  first  collected  empirically  from  observations  of  the 
planetary  motions,  and  afterwards  deduced  by  Newton  from 
the  Law  of  Gravitation  :  this,  then,  was  the  Inverse  Method  ; 


]l 


COMBINED  INDUCTION  AND  DEDUCTION     201 

but  the  result  is  something  very  different  from  any  that  can  be 
obained  by  the  Historical  Method.  The  essential  difference 
between  the  Physical  and  Historical  Methods  is  that,  in  the 
former,  w^hether  Direct  or  Inverse,  the  deductive  process, 
when  complete,  amounts  to  exact  demonstration  ;  whereas,  in 
the  latter,  the  deductions  consist  of  qualitative  reasonings,  and 
the  results  are  indefinite.  They  establish — (i)  a  priori  a 
merely  probable  connection  between  the  phenomena  according 
to  the  empirical  law  (say,  between  City-democracy  and  fickle 
politics) ;  (2)  connect  this  with  other  historical  or  social 
generalisations,  by  showing  that  they  all  alike  flow  from  the 
same  causes,  namely,  from  the  nature  of  races  of  men  under 
certain  social  and  geographical  conditions ;  and  (3)  explain 
why  such  empirical  laws  may  fail,  according  to  the  differences 
that  prevail  among  races  of  men  and  among  the  conditions 
under  which  they  live.  Thus,  seeing  how  rapidly  excitement 
is  propagated  by  the  chatter,  grimacing,  and  gesticulation  of 
townsmen,  it  is  probable  enough  that  the  democracy  of  a  City- 
state  should  be  fickle  (and  arbitrary,  because  irresponsible). 
A  similar  phenomenon  of  panic,  sympathetic  hope  and  despair, 
is  exhibited  by  every  stock-exchange,  and  is  not  peculiar  to 
political  life.  And  when  political  opinion  is  not  manufactured 
solely  in  the  reverberating  furnace  of  a  city,  fickleness  ceases 
to  characterise  Democracy ;  and,  in  fact,  is  not  found  in 
Switzerland  or  the  United  States. 

This  is  called  the  Historical  Method,  then,  because  it  is 
more  useful  than  any  other  in  explaining  the  movements  of 
history,  and  in  verifying  the  generalisations  of  political  and 
social  science.  We  must  not,  however,  suppose  that  its  use  is 
confined  to  such  studies.  Only  a  ridiculous  pedantry  would 
allot  to  each  subject  its  own  method  and  forbid  the  use  of  any 
other ;  as  if  it  were  not  our  capital  object  to  establish  truth  by 
any  means.  Wherever  the  forces  determining  a  phenomenon 
are  too  numerous  or  too  indefinite  to  be  combined  in  a 
deductive  demonstration,  there  the  Historical  Method  is 
likely  to  be  useful;  and  this  seems  often  to  be  the  case  in 


202      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

Geology  and  Biology,  as  well  as  in  the  Science  of  History,  or 
Sociology,  and  its  various  subsidiary  studies. 

Consider  upon  what  causes  historical  events  depend :  the 
customs,  character,  and  opinions  of  all  the  people  concerned  ; 
the  organisation  of  their  government,  and  the   character   of 
their  religious  institutions  ;  the  development  of  industry  among 
them,  of  the  military  art,  of  fine  art,  literature  and  science; 
their  relations,   commercial,    political   and   social   with   other 
nations ;  the  physical  conditions  of  climate  and  geographical 
position  amidst  which  they  live.    Hardly  an  event  of  importance 
occurs  among  them  that  is  not,  directly  or  indirectly,  influenced 
by  every  one  of  these  circumstances,  and  that  does  not  react 
upon.     Now,  from  the  nature  of  the  Inductive  Methods,  it  is 
plain  that,  in  such  a  complex  and  tangled  situation  as  history 
presents,  no  satisfactory  employment  of  them  is  possible ;  for 
they  all  require  the  actual  or  virtual  isolation  of  the  pheno- 
menon under  investigation.      They  also  require  the  greatest 
attainable  immediacy  of  connection  between  cause  and  effect ; 
whereas  the  causes  of  social  events  may  accumulate  durmg 
hundreds  of  years.     Clearly,  therefore,  in  collecting  empirical 
laws  from  history,  only  very  rough  inductions  can  be  hoped 
for,  and  we  may  have  to  be  content  with  simple  enumera- 
tion.    Hence    the   importance   of  supporting    such   laws    by 
deduction  from  the  nature  of  the  case,  however  faint  a  pro- 
bability of  the  asserted  connection  is  thereby  raised ;  and  this 
even  if  each  law  is  valued  merely  for  its  own  sake.     Still  more, 
if  anything  worth  the  name  of  Historical  Science  is  to  be  con- 
structed, must  a  mere  collection  of  such  empiricisms  fail  to 
content   us;    and   the   only   way   to   give   these   a   scientific 
character  is  to  show  deductively  their  common  dependence 
upon  various  combinations  of  the  same   causes.     Yet   even 
those  who  profess  to  employ  the  Historical  Method  often  omit 
the  deductive  half  of  it;  and  of  course  '  practical  poHticians' 
boast  of  their  entire  contentment  with  what   they   call   '  the 

facts.' 
^  Sometimes,  however,  politicians,  venturing  upon  deductive 


«i 


COMBINED  INDUCTION  AND  DEDUCTION     203 

reasoning,  have  fallen  into  the  opposite  error  of  omitting  to 
test  their  resuhs  by  any  comparison  with  the  facts :  arguing 
from  certain  '  Rights  of  Man,'  or   *  Interests  of  Classes,'  or 
'  Laws  of  Supply  and  Demand,'  that  this   or   that  event   will 
happen,  or  ought  to  happen,  without  troubling  themselves  to 
observe  whether  it  does  happen  or  ever  has  happened.     This 
method  of  deduction  without  any   empirical   verification,   is 
called  by  Mill  the  Geometrical ;  and,  plainly,  it  can  be  trust- 
worthy only  where  there  is  no  actual  conflict  of  forces  to  be 
considered.      In   pure   mathematical  reasoning   about  space, 
time,  and  number,  provided  the  premises  and  the  reasoning 
be  correct,  verification  by  a  comparison  with  the  facts  may 
be  needless,  because  there  is  no  possibility  of  counteraction. 
But  when  we  deal  with  actual  causes,  no  computation  of  their 
effects  can  be  relied  upon  without  comparing  our  conclusions 
with  the  facts  :  not  even  in  Astronomy  and  Physics,  least  of 
all  in  Politics. 

Burke,   then,   has  well  said  that   "without  the  guide   and 
light  of  sound  well-understood  principles  all  our  reasoning  in 
politics,  as   in   everything   else,    would   be   only   a   confused 
jumble  of  particular  facts  and  details  without  the  means  of 
drawing  any  sort  of  theoretical  or  practical  conclusion  " ;  but 
that,  on  the  other  hand,  the  statesman,   who  does  not  take 
account  of  circumstances,  infinite  and  infinitely  combined,  "  is 
not  erroneous,  but  stark  mad."     There  is,  or  ought  to  be,  no 
logical  difi*erence  between  the  evidence  required  by  a  states- 
man and  that  appealed  to  by  a  philosopher ;  and  since,  as  we 
have  seen,  the  combination  of  principles  with  circumstances 
cannot,  in  solving  problems  of  social  science,  be  made  with 
the  demonstrative  precision  that  belongs  to  astronomical  and 
physical  investigations,  there  remains  the  Historical  Method  as 
above  described. 

Examples  of  the  empirical  laws  from  which  this  method  begins  will 
occur  to  every  one.  They  abound  in  histories,  newspapers,  and  political 
discussions,  atid  are  of  all  shades  of  truth  or  half-truth :  as  that  '  His- 
tory consists  in  the  biographies  of  great  men  '  ;  in  other  words,  that  the 


I 


204      LOCxIC:   DEDUCTIVE   AND   INDUCTIVE 

movements  of  society  are  due  to  exceptional  personal  powers,  not  to 
general  causes  ;  That  at  certain  epochs  great  men  occur  in  groups  ;  That 
every  Fine  Art  passes  through  periods  of  development,  culmination  and 
decline  ;  That  Democracies  tend  to  change  into  Despotisms ;  That  the 
possession  of  power,  whether  by  classes  or  despots,  corrupts  the  pos- 
sessor ;  That  '  the  governments  most  distinguished  for  sustained  vigour 
and  abilities  have  generally  been  aristocracies ' ;  That  '  revolutions 
always  begin  in  hunger ' ;  That  civilisation  is  inimical  to  individuality  ; 
That  the  civilisation  of  the  country  proceeds  from  the  town  ;  That  '  the 
movement  of  progressive  societies  has  hitherto  been  a  movement  from 
Status  to  Contract'  {i.e.,  from  a  condition  in  which  the  individual's  rights 
and  duties  depend  on  his  caste,  or  position  in  his  family  as  slave,  child, 
or  patriarch,  to  a  condition  in  which  his  rights  and  duties  are  largely 
determined  by  the  voluntary  agreements  he  enters  into) ;  and  this  last 
is  treated  by  Mr.  Spencer  as  one  aspect  of  the  law  first  stated  by 
Comte,    that   the   progress   of  societies   is   from   the   military   to   the 

industrial  state. 

The  deductive  process  we  may  illustrate  by  Mr.  Spencer's  explana- 
tion ci  priori  of  the  co-existence  in  the  military  state  of  those  specific 
characters,  the  inductive  proof  of  which  furnished  an  illustration  of  the 
method  of  Agreement.     The  type  of  the  military  State  involves  the 
growth  of  the  warrior  class,  and  the  treatment  of  labourers  as  existing 
solely  to  support  the  warriors ;  the  complete  subordination  of  all  indi- 
viduals to  the  will  of  the  despotic  soldier-king,  their  property,  liberty 
and  life  being  at  the  service  of  the  State  ;  the  regimentation  of  society, 
not  only  for  military,  but  also  for  civil  purposes  ;  the  suppression  of  all 
private  associations,  etc.    Now  all  these  characteristics  arise  from  their 
utility  for  the  purpose  of  war,  a  utility  amounting  to  necessity  if  war  is 
the  State's  chief  purpose.     For  every  purpose  is  best  served  when  the 
whole  available  force  co-operates  toward  it :  other  things  equal,  the 
bigger  the  army  the  better  ;  and  to  increase  it,  men  must  be  taken  from 
industry  until  only  just  enough  remain  to  feed  and  equip  the  soldiers. 
As  this  state  of  things  is  not  to  everybody's  taste,  there  must  be  despotic 
control ;  and  this  control  is  most  effective  through  regimentation  by 
grades  of  command.    I'rivate  associations,  of  course,  cannot  live  openly 
Tn  such  a  State,  because  they  may  have  wills  of  their  own  and  are  con- 
venient for  conspiracy.    Thus  the  induction  of  characteristics  is  verified 
by  a  deduction  of  them  from  the  nature  of  the  case. 

§  6.  The  greater  indefiniteness  of  the  Historical,  compared 
with  the  Physical  Method,  both  in  its  inductions  and  in  its 
deductions,  makes  it,  perhaps,  even  more  difficult  to  work 
with.  It  wants  much  sagacity  and  more  sincerity;  for  the 
demon  of  Party  is  generally  too  much  with  us.     Our  first  care 


'1 


COMBINED  INDUCTION  AND  DEDUCTION     205 

should  be  to  make  the  empirical  law  as  nearly  true  as 
possible,  collecting  as  many  as  we  can  of  the  facts  which 
the  law  is  supposed  to  generalise,  and  examining  them  according 
to  the  canons  of  Induction,  wdth  due  allowance  for  the  imperfect 
applicability  of  those  canons  to  such  complex,  unwieldy,  and 
indefinite  instances. 

Turning  to  the  examples  of  such  laws  given  above,  it  is 
clear  that  in  some  cases  no  pains  have  been  taken  to  examine 
the  facts.     What  is  the  inductive  evidence  that  Democracies 
change    into   Despotisms ;    that  revolutions   always  begin    in 
hunger  ;  or  that  civilisation  is  inimical  to  individuality  ?     Even 
Mill's  often  cjuoted  saying,  "  that  the  governments  remarkable 
in  history  for  sustained  vigour  and  ability  have  generally  been 
aristocracies",  is  oddly  over-stated.     For  if  you  turn  to  the 
passage  {J^e/>.  Gov.  chap,  vi.),  the  next  sentence  tells  you  that 
such  governments  have  always  been  aristocracies   of  public 
functionaries ;  and  the  next  sentence  but  one  restricts,  appa- 
rently, the  list  of  such  remarkable  governments  to  two — Rome 
and  Venice.     Whence,  then,  comes  the  word  "  generally  "  into 
Mill's  law  ? 

As  to  deducing  our  empirical  law  from  a  consideration  of 
the  nature  of  the  case,  it  is  obvious  that  we  ought — (a)  to 
take  account  of  all   the   important  conditions ;  (/^)  to  allow 
weight  to  them  severally  in  proportion  to  their  importance ; 
and  {c)  not  to  include  in  our  estimates  any  condition  which  we 
cannot  show  to  be  probably  present  and  operative.     Thus  the 
Great-Man-Theory    of  history   must   surely   be    admitted   to 
assign  a  real  condition  of  national  success.     The  great  man 
organises,  directs,  inspires :  is  that  nothing  ?     On  the  other 
hand,  to  recognise  no  other  condition  of  national  success  is  the 
manifest  frenzy  of  a  mind  in  the  mythopoeic  age.     We  must 
allow  the  great  man  his  due  weight,  and  then  inquire  into  the 
general  conditions  that  (a)  bring  him  to  birth  in  one  nation 
rather  than  another,  and  {d)  give  him  his  opportunity. 

Mill's  explanation  of  the  success  of  the  aristocratic  governments  of 
Rome  and  Venice  is,  that  they  were,  in  fact,  bureaucracies  ;  that  is  to 


2o6      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

say,  their  members  were  trained  in  the  science  and  art  of  administration 
and  command.      Here,  again,  we  have,  no  doubt,  a  real  condition  ;  but 
is  it  the  only  one?     The  public  mind,  which  little   relishes  the  scaling 
down  of  Mill's  original  law  to  those  two  remote  cases,  is  persuaded 
hat  an  aristocracy  is  the  depository  of  hereditary  virtue,  especially 
with  reference  to  government,  and  would  at  once  ascribe  to  this  circum- 
stance the  greater  part  of  the  success  of  any  aristocratic  government. 
Now,  if  the  effects  of  training  are  inherited,  they  must,  in  an  hereditary 
aristocracy,  increase  the  energy  of  the  cause  assigned  by  Mill ;  but,  if 
not,  such  heredity  is  a  condition  "  not  present  or  not  operative."     Still, 
if  families  are  ennobled  for  their  extraordinary  natural  powers  of  ad- 
ministration  or  command  (and  this  sometimes  happens),  it  is  agreed 
on  all  hands  that  innate  qualities  are  heritable  ;  at  least,  if  care  be 
taken  to  intermarry  with  families  similarly  distinguished,  and  if  by 
natural  or  artificial  selection  all  the  failures  among  the  offspring  be 
eliminated.     The  Spartans  had  some  crude  notion  of  both  these  pre- 
cautions ;  and  if  such  measures  had  been  widely  adopted,  we  might 
deduce  from  the  doctrine  of  heredity  a  probability  in  favour  of  Mill's 
original  proposition,  and  thereby  verify  it  in  its  generality,  if  it  could 
be  collected  from  the  facts. 

The   Historical   Method  may  be   further  illustrated   by  the  course 
adopted  in  that  branch  of  Social  Science  which  has  been  found  sus- 
ceptible   of    the    most   extensive   independent   development,   namely, 
Economics.     First,  by  way  of  contrast,  I  should  say  that  the  general, 
abstract,  or  theoretical  treatment  of  Economics  is  according  to  the 
Physical  Method  ;  because,  as  Mill  explains,  although  the  phenomena 
of  industry  are  no  doubt  influenced,  like  other  social  affairs,  by  all  the 
other  circumstances  of  Society,  government,  religion,  war,  art,  etc. ;  yet, 
where  industry  is  most  developed,  as  in  England  and  the  United  States, 
certain  special  causes  are  so  much  the  most  important  that,  for  the 
purpose  at  least  of  a  first  outline  of  the  science,  they  may  conveniently 
be  considered  as  the  only  ones.     These  causes  are  :  (i)  the  general  dis- 
position of  men  to  obtain  wealth  with  as  little  trouble  as  possible,  and 
(2)  to  spend  it  so  as  to  obtain  the  greatest  satisfaction  of  their  various 
desires  ;  (3)  the  causes  that  determine  population,  and  (4)  the  tendency 
of  extractive  industry,  when  pushed  beyond  a  certain  limit  without  any 
improvement  in  the  industrial  arts,  to  yield   "diminishing  returns." 
From  these  causes  it  is  easy  to  infer  the  general  laws  of  prices,  of 
wages  and  interest  (which  are  the  prices  of  labour  and  of  the  use  of 
capital),  and  of  rent;  and  it  remains   to   verify  these   by  comparing 
them  with  the  facts  in  each  case ;  and  (if  they  fail  to  agree  with  the 
facts)  to  amend  them,  according  to  the  Method  of  Residues,  by  taking 
account  of  those  influential  causes  which  were  omitted  from  the  first 
draft  of  the  theory. 

Whilst,  however,  this  is  usually  the  procedure  of  those   inquirers 


'I 


COMBINED  INDUCTION  AND  DEDUCTION     207 

who  have  done  most  to  give  Economics  its  scientific  character,  to  insist 
that  no  other  plan  shall  be  adopted  would  be  sheer  pedantry ;  and  Dr. 
Keynes  has  shown,  in  his  Scope  and  Method  of  Political  Economy,  that 
Mill  has  himself  sometimes  solved  economic  problems  by  the  Historical 
Method.     With  an  analysis  of  his  treatment  of  Peasant  Proprietorship 
in  Book  n.,  cc.  7  and  8  of  his  Principles  of  Political  Economy,  we  may 
close  this  chapter.     Mill  first  shows  inductively,  by  collecting  evidence 
from   Switzerland.   Germany,   Norway.    Belgium,    and    France,    that 
peasant   proprietors   are   superhumanly   industrious,   intelligent   culti- 
vators, and  generally  intelligent  men,   prudent,  temperate,  and   inde- 
pendent, and  that  they  exercise  self-control  in  avoiding  improvident 
marriages.     This  group  of  empirical  generalisations  as  to  the  character 
of  peasant  proprietors  is  easily  deduced  from  the  nature  of  the  case : 
for  their  industry  is  a  natural  consequence  of  the  fact  that,  however 
much  they  produce,  it  is  all  their  own ;  they  cultivate  intelligently, 
because  for  generations  they  have  given  their  whole  mind  to  it ;  they 
are  generally  intelligent  men,  because  the  variety  of  work  involved  in 
small  farming,  requiring  foresight  and  calculation,  necessarily  promotes 
intelligence  ;  they  are  prudent,  because  they  have  something  to  save, 
and  by  saving  can  improve  their  station  and  perhaps  buy  more  land  ; 
they  are  temperate,  because  intemperance  is  incompatible  with  industry 
and  prudence  ;  they  are  independent,  because  secure  of  the  necessaries 
of  life,  and  from  having  property  to  fall  back  upon ;  and  they  avoid 
improvidence  in  marriage,  because  the  extent  and  fertility  of  their  fields 
is  always  plainly  before  them,  and  therefore  how  many  children  they 
can  maintain  is  easily  calculated.    The  worst  of  them  is  that  they  work 
too  hard  and  deny  themselves  too  much  ;  but,  over  the  greater  part  of 
the  world,  other  peasantry  work  too  hard  :  though  they  can  scarcely  be 
said  to  deny  themselves  too  much,  since  all  their  labour  for  others 
brings  them  no  surplus  to  squander  upon  self-indulgence. 


CHAPTER  XVIII 

HYPOTHESES 

§  I.  An    Hypothesis,    sometimes   employed    instead   of  a 
known  law,  as  a  premise  in  the  deductive   investigation   of 
nature,  is  defined  by  Mill  as  "any  supposition  which  we  make 
(either   without   actual   evidence,    or   on    evidence    avowedly 
insufticient)  in   order  to  endeavour  to  deduce  from   it   con- 
clusions in  accordance  with   facts   which   are   known  to   be 
real ;  under  the   idea   that   if  the   conclusions  to  which  the 
hypothesis  leads  are  known  truths,  the  hypothesis  itself  either 
must  be,  or  at  least  is  likely  to  be,  true."     The  deduction  of 
known  truths  from  an  hypothesis  is  its  Verification ;  and  when 
this  has  been  accomplished  in  a  good  many  cases,   and  there 
are  no  manifest  failures,  it  is  often  called  a  Theory  :  though 
this  term  is  also  used  for  the  whole  system  of  laws  of  a  certain 
class  of  phenomena,  as  when  Astronomy  is  called  the  '  theory 
of  the  heavens.'     Between  hypothesis  and  theory  in  the  former 
sense  no  distinct  line  can  be  drawn ;  for  the  complete  proof  of 
a  certain  speculation  may  take  a  long  time,  and  meanwhile 
the   gradually   accumulating   evidence   produces   in    different 
minds   very    different   degrees   of  satisfaction;    so    that    the 
sangume  begin  to  talk  of  'the  theory,'  whilst  the  melancholic 
continue  to  call  it  '  the  hypothesis.' 

An  Hypothesis  may  be  made  concerning  an  agent  (such  as 
the  ether),  or  a  collocation  (such  as  the  plan  of  our  solar 
system-whether  geocentric  or  heliocentric),  or  a  law  of  an 
agent's  operation  (as  that  light  is  transmitted  by  a  wave 
motion). 


II' 


HYPOTHESES  ^^ 

as^L'  T'™''  "!'.P'^"^"°"  °f  Light  involves  bcth  an  agent,  the  Ether 
as    an  all  pervading  elastic  fluid,  and  also  the  law  of  its  operation 

d  fi  itrrs  "xhe '"  ^''''  V'''''  ^°™  ^"^  >"«''™ 

nnite  velocity.     The  agreement  between  the  calculated  results  nf 

^^fZVT':s^^:''^r':'  ''-"^--^  oflghtt  .hi 

t  z  of  taXrLdf '^'prt^'-  '^  ^''  ^'  ''^  '"^  --  ^ 

bodies  on  the  Earth  MnnnQ  .     ,  ^^'""'  "^""'y'  ^^"l^'  f«"ing 

hypothesis  :as  thai  f^.ttLTtgrte  "Z^l^iT':^ 

-  rxn^ro^ -rnafrtt^^^^^^^^ 

was  the  centre  of  the  universe  and  L'm'  '"t"""^'  "'^'  °"  =^"'' 

.srT'J  :2ri.z  Lr,.7„"  ,r;rcr  ?*- 

positions  and  Drincinlps      «  tUo*  r      , ,    -^P^^^^^^es  as  to  their  dis- 

peculiarly  absurd  maxim  as  thl*'  *°"'1°°'  ""?"'«  motives'  is  a 
human  hfe.  To  iZ^'bad  m.r  °°.°"!f  "^^  °^  understanding 
probable,  is  to  be  Zt  ng  fn  the    I'^iffit     ' •^^'".^r  ^"  J"^'  ^^ 

subject  in  .  a  dry  light.'    Nor  can Te  ^  ^  ' i"  '.rn'^^  ""' 

selves'-  fnrQ^lf  i.T,^    1  J       .        '^^^   ^^  "^^P     judging  others  by  our- 

se!  out  lot t erp?e  h  tes  of  oth:"''  Tf"''  ^'-ting-point  wh'en  we 
combinations  o?  wh  ch  he  elents^f  .  "  ""''"''''"'  "'^  "'^"f"'" 
how  these  are  <^etertitrJ,Xb  eedtg^oTLTrS' '''^' T' 
various  conditions,  and  again  by  the  circuLl "rof  Lch  man'rUfe 

s":  hlitro7°ht2  "sthl^Tf  1^  imaginaZ^J'ifh 

oi  inought.     Such  should  be  the  equipment  of  the 

O 


2IO 


LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


historian,  who  pursues  the  same  method  of  hypothesis  when  he  attempts 
to  explain  (say)  the  state  of  parties  upon  the  Exclusion  Bill,  or  the 
policy  of  Louis  XI.  Problems  such  as  the  former  of  these  are  the 
easier  ;  because,  amidst  the  compromises  of  a  party,  personal  peculiari- 
ties obliterate  one  another,  and  expose  a  simple  scheme  of  human 
nature  with  fewer  fig-leaves.  Much  more  hazardous  hypotheses  are 
necessary  in  interpreting  the  customs  of  savages,  and  the  feelings  of  all 
sorts  of  animals.  Thus  the  method  of  our  every-day  thoughts  is 
identical  with  that  of  our  most  refined  speculations.  Literary  criticisms, 
a-ain.  abound  with  hypotheses:  e.g.,  as  to  the  composition  of  the 
Homeric  poems,  the  order  of  the  Platonic  dialogues,  the  authorship  of 
the  C^dmonic  poems,  or  the  Ossianic.  or  of  the  letters  of  Junius.  And 
in  all  these  cases  we  have  to  ask  whether  the  Hypothesis  accounts  for 
the  facts. 

§  2.  It  follows  from  the  definition  of  an  hypothesis  that 
none  is  of  any  use  that  does  not  admit  of  verification  (proof 
or  disproof),  by  comparing  the  results  that  may  be  deduced 
from  it  with  facts  or  laws.  If  so  framed  as  to  elude  every 
attempt  to  test  it  by  facts,  it  can  never  be  proved  by  them 
nor  add  anything  to  our  understanding  of  them. 

Suppose  that  a  conjurer  asserts  that  his  table  is  controlled  by  the 
spirit  of  your  deceased  relative  of  virtuous  memory,  and  makes  it  rap 
out  an  account  of  some  domestic  adventure  that  could  hardly  have 
been   expected   to  be  within  a  stranger's  knowledge.     So  far  good. 
Then   trying  again,  the  table  raps  out  some  absurd  blunder  about  your 
family  history  which  the  deceased  relative  could  not  have  committed ; 
but  the  conjurer  explains  that  '  a  lying  spirit'  sometimes  possesses  the 
table      Plainly,  this  amendment  of  the  hypothesis  makes  it  equally 
compatible  with  success  and  with  failure.    It  has  been  said  of  a  certain 
supposed  biological   agent,    "It  would   seem  that  by  a  little   skilful 
manipulation  it  can  be  made  to  account  for  anything  that  has  ever 
been  observed,  or  is  ever  likely  to  be  observed.     It  is  one  of  those  con- 
venient invisibles  that  will  do  anything  that  you  desire."     And  what- 
ever the  justice  of  this  criticism,  it  shows  a  sound  conception  of  what 
is  to  be  required  of  an  hypothesis.     Very  similar  was  the  case  of  the 
Ptolemaic  Astronomy  :  by  perpetual  tinkering  its  hypothesis  was  made 
to  correspond  with  accumulating  observations  of  the  celestial  motions  ; 
so  that,  until  the  telescope  was  invented,  it  may  be  said  to  have  been 
almost  unverifiable.     Consider,  again,  the  sociological  hypothesis,  that 
civil  order  was  at  first  founded  on  a  Contract  which  remains  binding 
upon  all  mankind :  this  is  reconcilable  with  the  most  opposite  institu- 
tions.    For  we  have  no  record  of  such  an  event ;  and  if  the  institutions 


HYPOTHESES 


211 


of  one  State  (say  the  British)  include  ceremonies,  such  as  the  corona- 
tion oath  and  oath  of  allegiance,  which  may  be  remnants  of  an  original 
contract,  they  may  nevertheless  be  of  comparatively  recent  origin: 
whereas  if  the  institutions  of  another  State  (say  the  Russian)  contain 
nothing  that  admits  of  similar  interpretation,  yet  traces  of  the  Contract 
once  existing  may  long  since  have  been  obliterated.  Moreover,  the 
actual  contents  of  the  contract  not  having  been  preserved,  every  ad- 
herent of  this  hypothesis  supplies  them  at  his  own  discretion,  'accord- 
ing to  the  dictates  of  Reason ' ;  and  so  one  derives  from  it  the  duty  of 
passive  obedience,  and  another  with  equal  cogency  establishes  the 
right  of  rebellion. 

To  be  verifiable,  then,  an  hypothesis  must  be  definite;  if 
somewhat  vague  in  its  first  conception  (which  is  reasonably  to 
be  expected),  it  must  become  definite  in  order  to  be  put  to 
the  proof.  But,  except  this  condition  of  verifiability,  and 
definiteness  for  the  sake  of  verifiability,  without  which  a 
proposition  does  not  deserve  the  name  of  an  hypothesis,  it 
seems  inadvisable  to  lay  down  rules  for  a  '  legitimate '  hypo- 
thesis. 

The  epithet  is  infelicitous.  It  suggests  that  the  Logician  makes  rules 
for  scientific  inquirers  ;  whereas  his  business  is  to  discover  the  princi- 
ples which  they,  in  fact,  employ  in  what  are  acknowledged  to  be  their 
most  successful  investigations.  If  he  did  make  rules  for  them,  and 
they  treated  him  seriously,  they  might  be  discouraged  in  the  exercise 
of  that  liberty  of  hypothesising,  which  is  the  condition  of  all  originality  ; 
whilst  if  they  paid  no  attention  to  him,  he  must  suffer  some  loss  of 
dignity.  To  say  that  a  '  legitimate  hypothesis '  must  explain  all  the 
facts,  at  least  in  the  department  for  which  it  is  invented,  is  decidedly 
discouraging.  No  doubt  it  may  be  expected  to  do  this  in  the  long  run 
when  (if  ever)  it  is  completely  established ;  but  this  may  take  a  long 
time.  Is  it  meanwhile  illegitimate  ?  Or  can  this  adjective  be  applied 
to  Newton's  corpuscular  theory  of  Light,  even  though  it  has  failed  to 
explain  all  the  facts  ? 

§  3.  Given  a  verifiable  hypothesis,  however,  what  constitutes 
proof  or  disproof? 

(i)  If  a  new  agent  be  proposed,  it  is  desirable  that  we 
should  be  able  directly  to  observe  it,  or  at  least  to  obtain 
some  evidence  of  its  existence  of  a  different  kind  from  the 
very  facts  which  it  has  been  invented  to  explain.     Thus,  in  the 


212      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

discovery  of  Neptune,  after  the  existence  of  such  a  planet 
outside  the  orbit  of  Uranus  had  been  conjectured  (to  account 
for  the  movement  of  the  latter),  the  place  in  the  heavens  which 
such  a  body  should  occupy  at  a  certain  time  was  calculated, 
and  there  by  means  of  the  telescope  it  was  actually  seen. 

Agents,  however,  are  assumed  and  reasoned  upon  very  successfully 
which,  by  their  nature,  never  can  be  objects  of  perception :  such  are 
the  Atoms  of  Chemistry  and  the  Ether  of  Optics.  Hence,  the  severer 
Methodologists  regard  them  with  suspicion  :  Mill  was  never  completely 
convinced  about  the  ether.  He  was  willing,  however,  to  make  the 
most  of  the  evidence  that  has  been  adduced  as  indicating  a  certain  pro- 
perty of  it  distinct  from  those  by  which  it  transmits  radiation,  namely, 
mechanical  inertia,  whereby  it  has  been  supposed  to  retard  the  career 
of  the  heavenly  bodies,  as  shown  especially  by  the  history  of  Encke's 
comet.  This  comet  returns  sooner  than  it  should,  as  calculated  from 
the  usual  data  ;  and  this  may  be  due  to  the  influence  of  a  resisting 
medium  in  reducing  the  extent  of  its  orbit ;  and  such  a  medium  may 
be  the  Ether.  If  this  conjecture,  or  any  similar  one,  should  gain  accept- 
ance, the  Ether  might  be  regarded  as  a  vera  causa  (that  is,  a  condition 
whose  existence  may  be  proved  independently  of  the  phenomena  it  was 
intended  to  explain),  in  spite  of  its  being  excluded  by  its  nature  from 
the  sphere  of  direct  perception. 

After  all,  it  is  very  difficult,  you  know,  to  say  what  is  within  the 
sphere  of  direct  perception.  Waiving,  however,  this  question  (which  is 
far  from  elementary).  Science  is  not  a  way  of  perceiving  things,  but 
essentially  a  way  of  thinking  about  them.  It  starts,  indeed,  from  per- 
ception and  returns  to  it,  and  its  thinking  is  controlled  by  the  analogies 
of  perception.  Atoms  and  Ether  are  thought  about  as  if  they  could  be 
seen  or  felt ;  and  if  they  are  found  necessary  to  connect  and  explain 
perceptions,  those  who  can  understand  the  explanation  will  no  doubt  be 
reconciled  to  them.  For  most  men  of  Science,  I  suppose,  their  existence 
is  as  good  as  axiomatic. 

On  the  other  hand,  a  great  many  agents,  once  assumed  in  order  to 
explain  phenomena,  have  since  been  explained  away.  Of  course,  difact 
can  never  be  •  explained  away ' :  the  phrase  is  properly  applicable  to 
the  fate  of  erroneous  hypotheses,  when,  not  only  are  they  disproved, 
but  others  are  established  in  their  places.  Of  the  Aristotelian  spheres, 
which  were  supposed  to  support  and  translate  sun,  moon  and  planets, 
no  trace  has  ever  been  found  :  they  would  have  been  very  much  in  the 
way  of  the  comets.  Phlogiston,  again,  an  agent  much  in  favour  with 
the  earlier  Chemists,  was  found,  Whewell  tells  us,  when  their  theories 
were  tested  by  exact  weighing,  to  be  not  merely  non-existent  but  a 
minus  quantity ;  that  is  to  say,  it  required  the  assumption  of  its  absolute 


HYPOTHESES 


213 


lightness  "so  that  it  diminished  the  weight  of  the  compounds  into 
which  it  entered."  These  agents,  then,  have  been  explained  away,  and 
instead  of  them  we  have  gravitation  and  oxygen. 

(2)  Whether  the  hypothetical  agent  be  perceptible  or  not,  it 
cinnot  be  established,  nor  can  a  supposed  law  of  such  an 
agent  be  accepted  as  suf^cient  to  the  given  inquiry,  unless  it 
is  adequate  to  account  for  the  effects  which  it  is  called  upon  to 
explain,  at  least  so  far  as  it  pretends  to  explain  them.  The 
general  truth  of  this  is  sufficiently  obvious,  since  to  explain  the 
facts  is  the  purpose  of  an  hypothesis ;  and  we  have  seen  that 
Newton  gave  up  his  hypothesis  that  the  moon  was  a  falling 
body,  as  long  as  he  was  unable  to  show  that  the  amount  of  its 
deflection  from  a  tangent  (or  its  fall)  in  a  given  time,  was 
exactly  what  it  should  be,  if  the  Moon  was  controlled  by  the 
same  force  as  falling  bodies  on  the  Earth. 

It  is  worth  while,  however,  to  observe  the  limitations  to 
which  this  canon  is  subject.  In  the  first  place,  it  says  that, 
unless  adequate  to  explain  the  facts  in  question,  an  hypothesis 
cannot  be  ^established^ :  but,  for  all  that,  such  an  hypothesis 
may  be  a  very  promising  one. 

It  may  take  a  very  long  time  fully  to  verify  an  hypothesis.  Some 
facts  may  not  be  obtainable  that  are  necessary  to  show  the  connection 
of  others  :  as,  for  example,  the  hypothesis  that  all  species  of  animals 
have  arisen  from  earlier  ones  by  some  process  of  gradual  change,  can 
be  only  imperfectly  verified  by  collecting  the  fossil  remains  of  extinct 
species,  because  immense  depths  and  expanses  of  fossiliferous  strata 
have  been  destroyed.  Or,  again,  the  general  state  of  culture  may  be 
such  as  to  prevent  men  from  tracing  the  consequences  of  an  hypothesis  : 
for  which  reason,  apparently,  the  doctrine  that  the  Sun  is  the  centre  of 
our  planetary  system  remained  a  discredited  hypothesis  for  2000  years. 
Surely,  this  should  instruct  us  not  to  regard  an  hypothesis  as  necessarily 
erroneous  or  illegitimate  merely  because  we  cannot  yet  see  how  it 
works  out :  but  neither  can  we  in  such  a  case  regard  it  as  established, 
unless  we  take  somebody's  word  for  it. 

Secondly,  the  canon  says  that  an  hypothesis  is  not  estab- 
lished, unless  it  accounts  for  the  phenomena  so  far  as  it 
professes  to.  But  it  implies  a  complete  misunderstanding  to 
assail  a  doctrine  for   not   explaining    what    lies    beyond    its 


214      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

scope.  Thus,  it  is  no  objection  to  a  theory  of  the  origin  of 
species,  that  it  does  not  explain  the  origin  of  Ufe :  it  does  not 
profess  to.  For  the  same  reason,  it  is  no  objection  to  the 
theory  of  Natural  Selection,  that  it  does  not  account  for  the 
variations  which  selection  presupposes.  But  such  objections 
might  be  perfectly  fair  against  a  general  doctrine  of  Evolu- 
tion. 

An  interesting  case  in  Mr.  WaW^ce's  Darwinism  (chap,  x)  will  illustrate 
the  importance  of  attending  to  the  exact  conditions  of  an  hypothesis. 
He  says  that  in  those  groups  of  "birds  that  need  protection  from 
enemies.-   "when  the  male  is  brightly  coloured  and  the  female  sits 
exposed  on  the  nest,  she  is  always  less  brilliant  and  generally  of  quite 
sober  and  protective  hues";    and  his  hypothesis  is.  that  these  sober 
hues  have  been  acquired  or  preserved  by  Natural  Selection,  because  it 
is  important  to  the  family  that  the  sitting  bird  should  be  inconspicuous. 
Now  to  this  it  might  be  objected  that  in  some  birds  both  sexes  are 
brilliant  or  conspicuous ;  but  the  answer  is  that  the  female  of  such 
species  does  not  sit  exposed  on  the  nest;  for  the  nests  are  either  domed 
over  or  made  in  a  hole ;  so  that  the  sitting  bird  does  not  need  protective 
colouring.     If  it  be  objected,  again,  that  some  sober-coloured  birds 
build  domed  nests,  it  may  be  replied  that  the  proposition  •  All  con- 
spicuously coloured  birds  are  concealed  in  the  nest,'  is  not  to  be  con- 
verted simply  into  '  All  birds  that  sit  concealed  in  the  nest  are  con- 
spicuously coloured.'     In  the   cases   alleged   the   domed  nests  are  a 
protection  against  the  weather,  and  the  sober  colouring  is  a  general  pro- 
tection to  the  bird,  which  inhabits  an  open  country.     It  may  be  urged, 
however  that  jays,  crows  and  magpies  are  conspicuous  birds,  and  yet 
build  open  nests :  but  these  are  aggressive  birds,  not  needing  protection 
from  enemies.     Finally,  there  are  cases,  it  must  be  confessed,  in  which 
the  female  is  more  brilliant  than  the  male,  and  which  yet  have  open 
nests !     Yes :    but  then   the  muie  sits  upon  the  eggs,  and   the  female  is 
stronger  and  more  pugnacious ! 

Thus  every  objection  is  shown  to  imply  some  inattention  to  the  con- 
ditions of  the  problem  ;  and  in  each  case  it  may  be  said,  exceptio  prohat 
regulam-ihe  exception  tests  the  rule.  (Of  course,  the  usual  translation 
-proves  the  rule."  in  the  restricted  modern  senseof  "  prove."  is  absurd.) 
That  is  to  say,  it  appears  on  examination  ;  (i)  that  the  alleged  excep- 
tion is  not  really  one,  and  (2)  that  it  stands  in  such  relation  to  the  rule 
as  to  confirm  it.  For,  you  will  notice  that,  to  all  the  above  objections 
it  is  replied  that,  granting  the  phenomenon  in  question  (special  protec- 
tive colouring  for  the  female)  to  be  absent,  the  alleged  cause  (need  of 
protection)  is  also  absent ;  so  that  the  proof  is.  by  means  of  the  objections, 
extended  from  being  one  by  the  method  of  Agreement,  into  one  by  the 


HYPOTHESES 


215 


Double  Method.  Unfortunately.it  is  not  always  that  an  assailant's 
neglect  to  observe  the  exact  conditions  of  the  doctrine  m  dispute  can  be 
turned  to  such  good  account. 

Thirdly,  an  hypothesis  originally  intended  to  account  for 
the  whole  of  a  phenomenon  and  failing  to  do  so,  though  it 
cannot  be  established  in  that  sense,  may  nevertheless  contam 
an  essential  part  of  the  explanation. 

Thus  the  Neptunian  Hypothesis  in  Geology,  was  an  attempt  to 
explain  the  formation  of  the  Earth's  outer  crust,  as  havmg  been 
deposited  from  an  universal  ocean  of  mud.  In  the  progress  of  the 
science  other  causes,  seismic,  fluvial  and  atmospheric,  have  been  found 
necessary  in  order  to  complete  the  theory  of  the  history  of  the  Earth  s 
crust  •  but  it  remains  true  that  the  stratified  rocks,  and  some  that  have 
lost  their  stratified  character,  were  originally  deposited  under  water. 
Inadequacy,  therefore,  is  not  a  reason  for  entirely  rejecting  an  hypothesis 
or  treating  it  as  illegitimate. 

(3)  Granting  that  the  hypothetical  cause  is  real  and  ade- 
quate, the  investigation  is  not  complete.  Agreement  with  the 
facts  is  a  very  persuasive  circumstance,  the  more  so  the  more 
extensive  the  agreement,  especially  if  no  exceptions  are  known. 
Still  if  this  is  all  that  can  be  said  in  favour  of  an  Hypothesis,  it 
amounts  to  proof  by  the  Method  of  Agreement  only ;  it  does 
not  exclude  the  possibility  of  '  plural  causes ' ;  and  if  the 
Hypothesis  proposes  a  new  agent  that  cannot  be  directly 
observed,  it  may  be  possible  to  invent  another  Hypothesis, 
about  another  imagined  agent,  which  shall  be  equally 
plausible. 

According  to  Whewell,  it  is  a  strong  mark  of  the  truth  of  an  Hypo- 
thesis when  it  agrees  with  distinct  inductions  concerning  different 
classes  of  facts,  and  he  calls  this  the  •Consilience  »  I°.d""--' 
because  they  jump  together  in  the  unity  of  the  Hypothesis.  It  is 
particularly  convincing  when  this  Consilience  takes  place  easUy  and 
naturally  without  necessitating  the  mending  and  ""kering  of  the 
Hypothesis;  and  he  cites  the  Theory  of  Gravitation  and  he  Undula- 
tory  Theory  of  Light  as  the  most  conspicuous  examples  of  such  ever- 
vlcLrious  Hypotheses.  Thus,  Gravitation  explains  the  fal  of  bodies 
on  the  Earth,  and  the  orbits  of  the  planets  and  their  satellites,  .t 
applies  to  the  tides,  the  comets,  the  double  stars,  and  gives  consistency 
to  the  Nebular   Hypothesis,  whence  flow  important  Geological  infer- 


2i6      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


HYPOTHESES 


217 


ences;  and  all  this  without  any  need  of  amendment.  Nevertheless, 
Mill,  with  his  rigorous  sense  of  duty,  points  out,  that  an  induction  is 
merely  a  proposition  concerning  many  facts,  and  that  a  consilience  of 
inductions  is  merely  a  multiplication  of  the  facts  explained  ;  and  that, 
therefore,  if  the  proof  is  merely  agreement  in  each  case,  there  can  be 
no  more  in  the  totality  :  the  possibility  of  vicarious  causes  is  not  pre- 
cluded ;  and  the  hypothesis  may,  after  all,  describe  an  accidental  cir- 
cumstance. 

Whewell  also  laid  great  stress  upon  Prediction  as  a  mark  of  a  true 
Hypothesis.  Thus,  Astronomers  predict  eclipses,  occultations,  transits, 
long  beforehand  with  the  greatest  precision  ;  and  the  prediction  of  the 
place  of  Neptune  by  sheer  force  of  deduction  is  one  of  the  most 
astonishing  things  in  the  history  of  science.  Yet  Mill  persisted  in 
showing  that  a  predicted  fact  is  only  another  fact,  and  that  it  is  really 
not  very  extraordinary  that  an  hypothesis  that  happens  to  agree  with 
many  known  facts  should  also  agree  with  some  still  undiscovered. 
And,  I  must  say,  there  seems  to  be  some  illusion  in  the  common  belief 
in  the  probative  force  of  prediction.  Prediction  surprises  us,  puts  us  off 
our  guard,  and  renders  persuasion  easy  ;  in  this  it  resembles  the  force 
of  an  epigram  in  rhetoric.  Accordingly,  cases  can  be  produced  in 
which  erroneous  Hypotheses  have  led  to  prediction  ;  and  Whewell 
himself  produces  them.  Thus,  he  says  that  the  Ptolemaic  theory  was 
confirmed  by  its  predicting  eclipses  and  other  celestial  phenomena, 
and  by  leading  to  the  construction  of  Tables  in  which  the  places  of  the 
heavenly  bodie  were  given  at  every  moment  of  time.  Similarly,  both 
Newton's  theory  of  Light  and  the  Chemical  doctrine  of  Phlogiston  led 
to  predictions  which  came  true. 

What  sound  method  demands  in  the  proof  of  an  Hypo- 
thesis, then,  is  not  merely  that  it  be  shown  to  agree  with  the 
facts,  but  that  every  other  Hypothesis  be  excluded.  This,  to 
be  sure,  may  be  beyond  our  power ;  there  may  in  some  cases 
be  no  such  negative  proof  except  the  exhaustion  of  human 
ingenuity  in  the  course  of  time. 

The  present  theory  of  colour  has  in  its  favour  the  failure  of  Newton's 
corpuscular  hypothesis  and  of  Goethe's  anti-mathematical  hypothesis ; 
but  the  field  of  conjecture  remains  open.  On  the  other  hand,  Newton's 
proof  that  the  solar  system  is  controlled  by  a  central  force,  he  supported 
by  the  demonstration  that  a  force  having  any  other  direction  could  not 
have  results  agreeing  with  Kepler's  second  law  of  the  planetary  motions, 
namely,  that,  as  a  planet  moves  in  its  orbit,  the  areas  described  by  a 
line  drawn  from  the  sun  to  the  planet  are  proportional  to  the  times 
occupied  in  the  planet's  motion.  When  a  planet  is  nearest  to  the  sun, 
the  area  described  by  such  a  line  is  least  for  any  given  distance  traversed 


by  the  planet ;  and  then  the  planet  moves  fastest :  when  the  planet  is 
furthest  from  the  sun,  the  area  described  by  such  a  line  is  greatest  for 
an  equal  distance  traversed  ;  and  then  the  planet  moves  slowest.  This 
law  may  be  deduced  from  the  hypothesis  of  a  central  force,  but  not 
from  any  other ;  the  proof,  therefore,  as  Mill  says,  satisfies  the  method 
of  Difference. 

Apparently,  to  such  completeness  of  demonstration  certain 
conditions  are  necessary :  the  possibilities  must  lie  between 
alternatives,  such  as  A  or  not-A,  or  amongst  some  definite  list 
of  cases  that  may  be  exhausted,  such  as  equal,  greater  or  less. 
He  whose  hypothesis  cannot  be  brought  to  such  a  definite 
issue,  must  try  to  refute  whatever  other  hypotheses  are  offered, 
and  naturally  he  will  attack  first  the  strongest  rivals.  With 
this  object  in  view  he  looks  about  for  a  "  crucial  instance," 
that  is,  an  observation  or  experiment  that  stands  like  a  cross 
(sign-post)  at  the  parting  of  the  ways  to  guide  us  into  the  right 
way,  or,  in  plain  words,  an  instance  that  can  be  explained  by 
one  hypothesis  but  not  by  another. 

Thus  the  phases  of  Venus,  similar  to  those  of  the  Moon,  but  con- 
curring with  great  changes  of  apparent  size,  when  discovered  by  Galileo, 
presented  a  crucial  instance  in  favour  of  the  Copernican  hypothesis,  as 
against  the  Ptolemaic,  so  far  at  least  as  to  prove  that  Venus  revolved 
around  the  Sun  inside  the  orbit  of  the  Earth.  Foucault's  experiment 
determining  the  velocity  of  Light  (cited  in  the  last  chapter)  was  at  first 
intended  as  an  experimentum  crucis  to  decide  between  the  corpuscular  and 
undulatory  theories ;  and  answered  this  purpose,  by  showing  that  the 
velocity  of  a  beam  passed  through  water  was  less  than  it  should  be 
by  the  former,  but  in  agreement  with  the  latter  doctrine  (Deschanel : 

§813). 

Perhaps  experiments  of  this  decisive  character  are  commonest  in 
Chemistry:  chemical  tests,  says  Herschel,  "are  almost  universally 
crucial  experiments."  The  following  is  abridged  from  Playfair  [Encycl. 
Met.,  Diss.  HI) :  The  Chemists  of  last  century  observed  that  metals 
were  rendered  heavier  by  calcination ;  and  there  were  two  ways  of 
accounting  for  this  :  either  something  had  been  added  in  the  process, 
though  what  they  could  not  imagine  ;  or,  something  had  been  driven 
off  that  was  in  its  nature  light,  namely.  Phlogiston.  To  decide  between 
these  hypotheses,  Lavoisier  hermetically  sealed  some  tin  in  a  glass 
retort,  and  weighed  the  whole.  He  then  heated  it  ;  and,  when  the  tin 
was  calcined,  weighed  the  whole  again,  and  found  it  the  same  as  before. 
No  substance,  therefore,  either  light  or  heavy,  had  escaped.    Further, 


\ 


2i8      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

when  the  retort  was  cooled  and  opened,  the  air  rushed  in,  showing 
that  some  of  the  air  formerly  within  had  disappeared  or  lost  its  elasticity. 
On  weighing  the  whole  again,  its  weight  was  now  found  to  have  in- 
creased by  ten  grains  ;  so  that  ten  grains  of  air  had  entered  when  it  was 
opened.  The  calcined  tin  was  then  weighed  separately,  and  proved  to 
be  exactly  ten  grains  heavier  than  when  it  was  placed  in  the  retort  ; 
showing  that  the  ten  grains  of  air  that  had  disappeared  had  combined 
with  the  metal  during  calcination.  This  experiment,  then,  decided 
against  Phlogiston,  and  led  afterwards  to  an  analysis  of  common  air 
confirming  Priestley's  discovery  of  oxygen. 

§  4.  We  have  now  seen  that  an  Hypothesis  must,  to  deserve 
the  name  in  Science,  be  verifiable  and  therefore  definite ;  and 
that  to  establish  itself  as  a  true  theory,  it  must  present  some 
symptom  of  reality,  and  be  adequate  and  unconditional. 
Thus  guarded.  Hypotheses  seem  harmless  enough;  but, 
certainly,  people  sometimes  have  a  strong  prejudice  against 
them,  as  against  a  tribe  of  savages  without  government,  or 
laws,  or  any  decent  regard  for  vested  interests.  It  is  well 
known,  too,  that  Bacon  and  Newton  disparaged  them.  But 
Bacon  in  his  examples  of  an  investigation  according  to  his 
own  method,  is  obliged  after  a  preliminary  classification  of 
facts,  to  resort  to  an  hypothesis,  calling  it  permissio  iutelledus, 
interpretatio  inchoata  or  vindemiatio  prima.  And  what  Newton 
meant  by  hypotheses  ?ion  Jingo,  seeing  that  he  invented  so  many, 
is  itself  fair  game  for  an  hypothesis.  At  any  rate,  it  is  plain 
that  hypotheses  are  essential  aids  to  discovery:  indeed, 
speaking  generally,  deliberate  investigation  depends  wholly 
upon  the  use  of  them. 

It  is  true  that  we  may  sometimes  observe  a  train  of  events  that 
chances  to  pass  before  us,  either  when  we  are  idle  or  engaged  with 
some  other  inquiry,  and  so  obtain  a  new  glimpse  of  the  course  of 
nature.  Or  we  may  try  experiments  haphazard,  and  watch  the  results. 
But,  even  in  these  cases,  before  our  new  notions  can  be  considered 
knowledge,  they  must  be  definitely  framed  in  hypotheses  and  re- 
observed  or  experimented  upon,  with  whatever  calculations  or  pre- 
cautions may  be  necessary  to  ensure  accuracy  or  isolation.  As  a  rule, 
however,  when  inquiring  deliberately  into  the  cause  of  an  event, 
whether  in  nature  or  in  history,  we  first  reflect  upon  the  circumstances 
of  the  case  and  compare  it  with  similar  ones  previously  investigated 


HYPOTHESES 


219 


and  so  are  guided  by  a  preconception  more  or  less  definite  of  '  what 
to  look  for,'  what  the  cause  is  likely  to  be,  that  is,  by  an  hypothesis. 
Then,  if  our  preconception  is  justified,  or  something  which  we  observe 
leads  to  a  new  hypothesis,  either  we  look  for  other  instances  to  satisfy 
the  canons  of  Agreement :  or  (if  the  matter  admits  of  experiment)  we 
endeavour,  under  known  conditions  according  to  the  canons  of  Differ- 
ence and  Variations,  to  reproduce  the  event  by  means  of  that  which 
our  hypothesis  assigns  as  the  cause;  or  we  draw  remote  inferences 
from  our  hypothesis,  and  try  to  test  these  by  the  Inductive  Canons. 

If  we  argue  from  an  hypothesis  and  express  ourselves  formally, 
it  will  usually  appear  as  the  Major  Premise;  but  this  is  not  always 
the  case.  In  extending  ascertained  laws  to  fresh  cases,  the  Minor 
Premise  may  be  an  hypothesis,  as  in  testing  the  chemical  constitution 
of  any  doubtful  substance,  such  as  a  piece  of  ore.  Some  solution  or 
preparation,  A,  is  generally  made  which  (it  is  known)  will,  on  the 
introduction  of  a  certain  agent,  B,  give  a  reaction,  C,  if  the  preparation 
contains  a  given  substance,  X.  The  major  premise,  then,  is  the  law  of 
reaction — 

Whenever  A  is  X,  if  treated  with  B  it  is  C. 
The  minor  premise  is  an  hypothesis  that  the  preparation  contains  X. 
An  experiment  then  treats  A   with  B.     If  C  results,  a  probability  is 
raised  in  favour  of  the  hypothesis  that  A  is  X ;  or  a  certainty,  if  we 
know  that  C  results  on  that  condition  only. 

So  important  are  hypotheses  to  science,  that  Whewell  insists  that 
they  have  often  been  extremely  valuable  even  though  erroneous.  Of 
the  Ptolemaic  system  he  says,  "  We  can  hardly  imagine  that  Astronomy 
could,  in  its  outset,  have  made  so  great  a  progress  lender  any  other 
form."  It  served  to  connect  men's  thoughts  on  the  subject  and  to 
sustain  their  interest  in  working  it  out;  by  successive  corrections 
"to  save  appearances,"  it  attained  at  last  to  a  descriptive  sort  of 
truth,  which  was  of  great  practical  utility ;  it  also  occasioned  the 
invention  of  technical  terms,  and,  in  general,  digested  the  whole  body 
of  observations  and  prepared  them  for  assimilation  by  a  better  hypo- 
thesis in  the  fulness  of  time.  Whewell  even  defends  the  maxim  that 
"Nature  abhors  a  vacuum,"  as  having  formerly  served  to  connect 
many  facts  that  differ  widely  in  their  first  aspect.  "And  in  reality 
is  it  not  true,"  he  asks,  "that  nature  does  abhor  a  vacuum,  and  does 
all  she  can  to  avoid  it  ?  "  Let  no  forlorn  cause  despair  of  a  champion  ! 
Yet  no  one  has  accused  Whewell  of  Quixotry ;  and  the  sense  of  his 
position  is  that  the  human  mind,  of  course,  is  a  rather  feeble  affair, 
which  can  hardly  begin  thinking  except  with  blunders. 

The  progress  of  Science  may  be  plausibly  attributed  to  a  process  of 
Natural  Selection  :  Hypotheses  are  produced  in  abundance  and  variety, 
and  those  unfit  to  bear  verification  are  destroyed,  until  only  the  fittest 
survive.     Wallace,  a  practical  naturalist,  if  there  ever  was  one,  as  well 


~r«~ 


I    W,W 


220 


LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


HYPOTHESES 


221 


as  an  eminent  theorist,  takes  the  same  view  as  Whewell  of  such  in- 
adequate conjectures.  Of  '  Lemuria,'  a  hypothetical  continent  in  the 
Indian  Ocean,  once  supposed  to  be  traceable  in  the  islands  of  Mada- 
gascar, Seychelles  and  Mauritius,  its  surviving  fragments,  and  named 
from  the  Lemurs,  its  characteristic  denizens,  he  says  {Island  Life, 
chap,  xix.)  that  it  was  "essentially  a  provisional  hypothesis,  very 
useful  in  calling  attention  to  a  remarkable  series  of  problems  in 
geographical  distribution  [of  plants  and  animals],  but  not  affording 
the  true  solution  of  those  problems."  We  see,  then,  that  '  provisional 
hypotheses,'  though  erroneous,  may  be  very  useful  or  (as  Whewell 
says)  necessary. 

Hence,  to  be  prolific  of  hypotheses  is  the   first  attribute 
of  scientific  genius ;  the  first,  because  without  it  no  progress 
whatever    can    be    made.      And  some  men  seem  to  have  a 
marked  felicity,  a  sort  of  instinctive  judgment  even  in  their 
guesses,  as  if  their  heads  were  made   according   to   Nature. 
But  others  among  the  greatest,  like  Kepler,  guess  often  and 
are  often  wrong  before  they  hit   upon   the   truth,  and   them- 
selves, like  Nature,  destroy  many  vain  shoots  and  seedUngs  of 
science  for  one  that  they  find  fit  to  live.     If  this  is  how  the 
mind  works  in  scientific  inquiry  (as  it  certainly  is,  with  most 
men,  in  poetry,  in  fine  art,  and  in  the  scheming  of  business),  it 
is  useless  to  repine.     We  should  rather  recognise  a  place  for 
fool's  hypotheses,  as  Darwin  did  for  '•  fool's  experiments." 

But  to  complete  the  scientific  character,  there  must  be  great 
patience,  accuracy,  and  impartiality  in  examining  and  testing 
these  conjectures,  as  well  as  great  ingenuity  in  devising 
experiments  to  that  end.  It  is  the  want  of  these  qualities 
that  leads  to  crudity  and  public  failure  and  brings  hypotheses 
into  derision.  Not  partially  and  hastily  to  believe  in  one's 
own  guesses,  nor  petulantly  and  hastily  to  reject  them,  but 
to  consider  the  matter,  to  suspend  judgment,  is  the  moral 
lesson  of  science  :  difficult,  distasteful,  and  rarely  mastered. 

Everybody,  according  to  his  lights,  makes  haste  to  frame  hypotheses, 
whether  for  scientific  or  private  uses  ;  because,  as  Whewell  says,  "  man 
is  prone  to  become  a  deductive  reasoner,"  and  hypotheses,  anticipating 
the  laborious  induction  of  highly  general  laws,  are  a  short  cut  to 
deduction.     There  are   two  sides   to  this  proneness  of  our   nature, 


/ 


a  good  and  a  bad.  The  good  is  that  hypothesis  and  deduction 
have  in  fact  been  the  great  means  of  explaining  or  enabling  us  to 
understand  the  world ;  so  that  our  instinctive  resort  to  them  is  a 
predisposition  to  Science.  The  bad  is  that  this  method  encourages 
superficiality.  Deduction  is  generally  easier  than  Induction,  because 
it  is  carried  on  far  more  by  means  of  signs,  whether  in  Mathematics 
or  common  language.  To  wield  the  higher  Mathematics  needs  a  dis- 
tinguished head ;  but  this  power  cannot  be  put  into  competition  with 
the  distinct  and  comprehensive  imagination  necessary  to  represent 
masses  of  facts  for  inductive  analysis.  For  the  great  use  of  language 
and  of  all  symbols  in  thinking,  is  to  economise  this  energy  of  imagina- 
tion. Without  such  devices  the  human  race  could  never  have  developed : 
for  who  can  imagine  the  purport  in  denotation  of  a  single  general 
name  ?  But  these  devices  show  '  the  defects  of  their  qualities '  by 
often  quite  superseding  thought  and  degenerating  into  gibberish. 
Whether,  indeed,  this  is  ever  true  of  the  higher  Mathematics  is  not 
for  me  to  say ;    but  everybody  knows  how  true  it  is  of  common  speech. 

§  5.  The  word  Hypothesis  is  often  also  used  for  the  scientific 
device  of  treating  an  Abstraction  as,  for  the  purposes  of  argu- 
ment, equivalent  to  the  concrete  facts.  Thus,  in  Geometry,  a 
line  is  treated  as  having  no  breadth ;  in  Mechanics,  a  bar  may 
be  supposed  absolutely  rigid,  or  a  machine  to  work  without 
friction ;  in  Economics  (as  we  saw  in  the  last  chapter),  man 
is  sometimes  regarded  as  actuated  solely  by  love  of  gain  and 
dislike  of  exertion.  The  results  reached  by  such  reasoning 
may  be  made  applicable  to  the  concrete  facts,  if  allowance  be 
made  for  the  omitted  circumstances  or  properties,  in  the 
several  cases  of  lines,  bars,  and  men ;  but  otherwise  all  con- 
clusions from  abstract  terms  are  limited  by  their  definitions. 
Abstract  reasoning,  then  (that  is,  reasoning  limited  by  defini- 
tions), is  often  said  to  imply  *  the  hypothesis '  that  things  exist 
as  their  names  are  defined,  having  no  properties  but  those 
enumerated  in  their  definitions.  This  seems,  however,  a 
needless  and  confusing  extension  of  the  term ;  for  an 
hypothesis  proposes  an  agent,  collocation,  or  law  hitherto 
unknown ;  whereas  abstract  reasoning  proposes  to  exclude 
from  consideration  a  good  deal  that  is  well  known.  There 
seems  no  reason  why  the  latter  device  should  not  be  plainly 
called  an  Abstraction. 


^^^      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

Such  Abstractions  are,  of  course,  also  necessary  to  Science; 

rtre   lleTo   L\e   strange   blunders   by   mistaking  the 
character  of   the  results :  treating  the  results  as  simply  tru- 
actu':.  things,  instead  of  as  true  of  actual  th.ngs  only  so  fa 
as  they  are  represented  by  the  Abstractions.     In  addressing 
Thslict    reasoning,   therefore,    to   those   especially   .^o   a  e 
unfamiliar  with  scientific  methods,  pains  shou  d  ^e  taken  to 
make  it  clear  what  the  Abstractions  are,  what  are  the  con 
Tequen     imitations  upon  the  argument  and  its  conclusions 
a^d  what  corrections  and  allowances  are  necessary  in  orderjo 
make  the  conclusions  into  an  adequate  account  of  the  concrete 
fact      The  greater  the  number,  variety,  and  subtlety  o    the 
properties  possessed  by  any  object  (such  as  human  nature) 
Ae  '    ater  the   qualifications  required  in  the  conclusions  o 
abstrlTreasoning,  before  they  can  hold  true  of  such  an  object 

"ciosettn^^^^^^^^  this  method  of  Abstraction  is  the  Mathe- 
JS  Melhod  of  Limits.  In  his  History  of  Scientific  Meas 
(B   II.  c.  12),  Whewellsays: 

of  straight  lines,  and  theretore  ^^  '         ^     j  ^^y  curve. 

aoctrines  '>^  ^^X^^- ^rZ^^Z^:,!.' cu...  b/putting 
But  we  may  make  up  a  ngure  1  c     y  polygonal  building   of 

,.,ether  -^^^f^^tX^:^^^Zirr'Jr..    And  in  order 

;- Portr/nd  neaL  to  a  c„„  ^:^^X^^^ 
and  more  small,  more  and  more  ""'"^™"^.  ';,%i^^3;  ^n^aii  lines  to 
find  some  mode  of  measurement  some  ^^'^t'™  "^^^^^^      j^e  sides. 

r  ""trf^  'i:Ztt^t^s':::ST:^'-^^  equivalent  to 
however  far  it  be  carriea  ^  .,•„    ^he  sides  we  may  approach 

r,,<:.acnrin?  the  curve  itselt ,  tor  d>  muiupiyi"5  .  j:«-^,.^nrp» 

measuring  uie  ^u  appreciable  ditlerence 

"°'^^"%Te"cutTCis  tLT^:^/!^  /Xgon;  and  in  this 
;re:s\e  procX^^^^^^^  A^ion,  that  .What  is  true  up  to  the  Limit 
is  true  at  the  Limit.'  " 


HYPOTHESES 


223 


Now,  what  Whewell  calls  the  Axiom  here,  others  might  call 
an  Hypothesis;  but  perhaps  it  is  properly  a  Postulate.  And 
it  is  just  the  obverse  of  the  Postulate  implied  in  the  Method  of 
Abstractions,  namely,  that  '  What  is  true  of  the  Abstraction  is 
true  of  concrete  cases  the  more  nearly  they  approach  the 
Abstraction.'  What  is  true  of  the  '  Economic  Man '  is  truer 
of  a  broker  than  of  a  farmer,  of  a  farmer  than  of  a  labourer,  of 
a  labourer  than  of  the  artist  of  romance.  Hence  the  Abstrac- 
tion may  be  called  a  Limit  or  limiting  case,  in  the  sense  that 
it  stands  to  concrete  individuals,  as  a  curve  does  to  the  figures 
made  up  "by  putting  together  many  short  straight  lines." 
Correspondingly,  the  Proper  Name  may  be  called  the  Limit 
of  the  class- name  ;  since  its  attributes  are  infinite,  whereas  any 
name  whose  attributes  are  less  than  infinite  stands  for  a 
possible  class.  In  short,  for  logical  purposes,  a  Limit  may 
be  defined  as  any  extreme  case  to  which  actual  examples  may 
approach  without  ever  reaching  it.  And  in  this  sense 
'  Method  of  Limits '  might  be  used  as  a  term  including  the 
Method  of  Abstractions ;  though  it  would  be  better  to  speak 
of  them  generically  as  *  Methods  of  Approximations.' 

It  is  easy  to  conceive  of  an  objector  urging  that  such 
devices  as  the  above  are  merely  ways  of  avoiding  the  actual 
problems,  and  that  they  display  more  cunning  than  skill.  But 
Science,  like  good  sense,  puts  up  with  the  best  that  can  be 
had ;  and,  like  prudence,  does  not  reject  the  half-loaf.  The 
position,  that  a  conceivable  case  that  can  be  dealt  with  may, 
under  certain  conditions,  be  substituted  for  one  that  is 
unworkable,  is  a  touchstone  of  intelligence.  To  stand  out  for 
ideals  that  are  known  to  be  impossible,  is  only  an  excuse  for 
doing  nothing  at  all. 

In  another  sense,  again,  the  whole  of  Science  is  sometimes 
said  to  be  hypothetical,  because  it  takes  for  granted  the 
Uniformity  of  Nature ;  whilst  this,  in  its  various  aspects,  can 
only  be  directly  ascertained  by  us  as  far  as  our  experience 
extends ;  whereas  the  whole  value  of  the  principle  of 
Uniformity   consists    in    its    furnishing    a    formula    for    the 


224      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

extension  of  our  other  beliefs  beyond  our  actual  experience. 
Transcendentalists,  indeed,  call  it  a  form  of  Reason,  just 
because  it  is  presupposed  in  all  knowledge ;  and  they  and 
the  Empiricists  agree  that  to  adduce  material  evidence  for 
it,  in  its  full  extent,  is  impossible.  If,  then,  material  evidence 
is  demanded  by  any  one,  he  cannot  regard  the  conclusions  of 
Mathematics  and  physical  Science  as  depending  on  what  is 
itself  unproved ;  he  must,  with  Mill,  regard  these  conclusions 
as  drawn  "  not  from  but  according  to"  the  axioms  of  Equality 
and  Causation.  That  is  to  say,  if  the  axioms  are  true,  the 
conclusions  are;  the  material  evidence  for  them  being  the 
same,  namely,  uncontradicted  experience.  Now  when  we 
say,  '  If  Nature  is  uniform,  Science  is  true ',  the  hypothetical 
character  of  Science  appears  in  the  form  of  the  statement. 
Nevertheless,  it  seems  undesirable  to  call  our  confidence  in 
Nature's  uniformity  an  '  hypothesis ' :  it  is  incongruous  to  use 
the  same  term  for  our  tentative  conjectures  and  for  our  most 
indispensable  beliefs.  '  The  Universal  Postulate  '  is  a  better 
term  for  the  principle  which,  in  some  form  or  other,  every 
generalisation  takes  for  granted. 


CHAPTER  XIX 

LAWS  CLASSIFIED;  EXPLANATION;  CO-EXISTENCE; 

ANALOGY 


§  I.  Laws  are  classified,  according  to  their  degrees  of 
generality,  as  higher  and  lower,  though  the  grades  may  not 
be  decisively  distinguishable. 

First,  there  are  Axioms  or  Principles,  that  is  real,  universal, 
self-evident  propositions.  They  are— (i)  real  propositions; 
not,  like  'The  whole  is  greater  than  any  of  its  parts,' 
merely  definitions,  or  implied  in  definitions.  (2)  They  are 
universally  true  of  phenomena,  as  far  as  the  form  of  their 
expression  extends;  that  is,  for  example.  Axioms  concerning 
quantity  are  true  of  everything  that  is  considered  in  its 
quantitative  aspect,  though  not  (of  course)  in  its  qualitative 
aspect.  (3)  They  are  self-evident;  that  is,  each  rests  upon 
its  own  evidence  (whatever  that  may  be);  they  cannot  be 
derived  from  one  another,  nor  from  any  more  general  law. 
Some,  indeed,  are  more  general  than  others:  the  Logical 
Principle  of  Contradiction,  *  If  A  is  B,  it  is  not  not-B ',  is 
true  of  qualities  as  well  as  of  quantities;  whereas  the 
Axioms  of  Mathematics  apply  only  to  quantities.  The 
Mathematical  Axioms,  again,  apply  to  Time,  Space,  Mental 
phenomena,  and  Matter  and  Energy;  whereas  the  Law  of 
Causation  is  only  true  of  concrete  events  in  the  redistribu- 
tion of  Matter  and  Energy :  such,  at  least,  is  the  strict  limit 
of  Causation,  if  we  identify  it  with  the  Conservation  of 
Energy  ;  although  our  imperfect  knowledge  of  Life  and  Mind 
often  drives   us   to    speak    of    feelings,    ideas,    volitions,    as 

p 


226      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

causes.  Still,  the  Law  of  Causation  cannot  be  derived  from 
the  Mathematical  Axioms,  nor  these  from  the  Logical.  The 
kind  of  evidence  upon  which  Axioms  rest,  or  whether  any 
evidence  can  be  given  for  them,  is  (as  before  observed)  a 
question  for  Metaphysics,  not  for  Logic.  Axioms  are  the 
upward  limit  of  Logic,  which,  like  all  the  Special  Sciences, 

takes  them  for  granted. 

Next  to  Axioms,  come  Primary  Laws  of  Nature :  these  are 
of  less  generality  than  the  Axioms,  and  are  subject  to  the 
conditions  of  methodical  proof;  being  universally  true  only 
of  certain  forces  or  properties  of  matter,  or  of  nature  under 
certain  conditions ;  so  that  proof  of  them  by  logical  or 
mathematical  reasoning  is  expected,  because  they  depend  upon 
the  Axioms  for  their  formal  evidence.  Such  is  the  law  of 
Gravitation,  in  Astronomy ;  the  law  of  Heredity,  in  Biology ; 
in  Psychology,  the  law  of  Relativity. 

Then,   there  are  Secondary  Laws,  of   still  less  generality, 
resulting  from  a  combination  of  primary  conditions  or  forces 
in  given  circumstances,  and  therefore  conceivably  derivable 
from    the    laws    of   those   conditions    or    forces,    if   we    can 
discover  them  and  compute  their  united  effects.     Accordingly, 
Secondary    Laws    are    either— (i)    Derivative,    having    been 
analysed  into,  and  deduced  from,  Primary  Laws;  or  (2)  Em- 
pirical, those  that  have  not  yet  been  deduced  (though  from 
their  comparatively  special  and  complex  character,  it  seems 
probable  they  may  be,  given  sufficient  time  and  ingenuity), 
and  that  meanwhile   rest   upon   some  unsatisfactory  sort   of 
induction  by  Agreement  or  Simple  Enumeration. 

Whether  laws  proved  only  by  the  canon  ^f  Difference  are  to  be 
considered  Empirical,  is  perhaps  a  question  :  their  proof  derives  them 
from  the  principle  of  Causation ;  but.  being  of  narrow  scope,  some 
more  special  account  of  them  seems  requisite  in  relation  to  the  Primary 
Laws  before  we  can  call  them  Derivative  in  the  technical  sense. 

Many  Secondary  Laws,  again,  are  partially  or  imperfectly  Derivative : 
we  can  give  general  reasons  for  them,  without  being  able  to  determme 
theoretically  the  precise  relations  of  the  phenomena  they  describe. 
Thus  Meteorologists  can  explain  the  general  conditions  of  all  sorts  of 


LAWS   CLASSIFIED 


227 


weather,  but  have  made  but  little  progress  toward  predicting  the  actual 
course  of  it  (at  least,  for  our  island) :  Geologists  know  the  general  causes 
of  mountain  ranges,  but  not  why  they  rise  just  where  we  find  them : 
Economists  explain  the  general  course  of  a  commercial  crisis,  but  not 
why  the  great  crises  recur  at  intervals  of  about  ten  years. 

Derivative  Laws  make  up  the  body  of  the  exact  Sciences,  having 
been  assimilated  and  organised ;  whilst  Empirical  Laws  are  the  undi- 
gested materials  of  Science.  The  theorems  of  Euclid  are  good  examples 
of  Derivative  Laws  in  Mathematics ;  in  Astronomy,  Kepler's  laws  and 
the  laws  of  the  tides ;  in  Physics,  the  laws  of  shadows,  of  perspective, 
of  harmony  ;  in  Biology  the  law  of  Natural  Selection,  and  others  from 
this  ;  in  Economics,  the  laws  of  prices,  rents,  wages,  interest. 

Empirical  Laws  are  such  as  Bodes  law  of  the  planetary  distances ; 
the  laws  of  the  expansion  of  different  bodies  by  heat,  and  formulae 
expressing  the  electrical  conductivity  of  each  substance  as  a  function 
of  the  temperature.  Strictly  speaking,  1  suppose,  all  the  laws  of 
chemical  combination  are  Empirical :  the  law  of  definite  proportions 
is  found  true  in  all  cases  that  have  been  examined,  except  for  varia- 
tions that  may  be  ascribed  to  errors  of  experiment.  Much  the  same 
is  true  in  Biology  ;  most  of  the  secondary  laws  are  Empirical,  except  so 
far  as  structures  or  functions  may  be  regarded  as  specialised  cases  in 
Physics  or  Chemistry  and  deducible  from  these  Sciences.  The  theory 
of  Natural  Selection,  however,  has  been  the  means  of  rendering  many 
laws,  that  were  once  wholly  Empirical,  at  least  partially  Derivative; 
namely,  the  laws  of  the  Geographical  distribution  of  plants  and  animals, 
and  of  their  adaptation  in  organisation,  form  and  colour,  habits  and 
instincts,  to  their  various  conditions  of  life.  The  laws  that  remain 
Empirical  in  Biology  are  of  all  degrees  of  generality,  from  that  of  the 
tendency  to  variation  in  size  and  in  every  character  shown  by  all  (or 
nearly  all)  species  (though  as  to  the  reason  of  this  there  are  promising 
hypotheses),  down  to  such  curious  cases  as  that  the  colour  of  roses  and 
carnations  never  varies  into  blue,  that  scarlet  flowers  are  never  sweet- 
scented,  that  bullfinches  fed  on  hemp-seed  turn  black,  that  the  young  of 
white,  yellow  and  dun  pigeons  are  born  almost  naked  (whilst  others  have 
plenty  of  down);  and  so  on. 

A  '  Fact,'  in  the  common  use  of  the  word,  is  a  particular 
Observation  :  it  is  the  material  of  science  in  its  rawest  state. 
As  perceived  by  a  mind,  it  is,  of  course,  never  absolutely 
particular :  for  we  cannot  possibly  perceive  anything  without 
classing  it,  more  or  less  definitely,  with  things  already  known 
to  us ;  nor  describe  it  without  using  connotative  terms  which 
imply  a  classirication  of  the  things  denoted.     Still,  we  may 


428     LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

consider  an  Observation  as  particular,  in  Comparison  with  a 
Law  that  includes  it  with  numerous  others  in  one  general 
proposition.  To  turn  an  Observation  into  an  Experiment 
or  (where  experiment  is  impracticable)  to  repeat  it  with  all 
possible  precautions  and  exactness,  is  the  first  stage  ot 
scientific  manufacture.  Then  comes  the  formulation  of  an 
Empirical  law  ;  and  lastly,  if  possible,  deduction  or  derivation, 
either  from  higher  laws  previously  ascertained,  or  from  an 
hypothesis.  However,  as  a  word  is  used  in  various  senses, 
we  often  speak  of  laws  as  'facts':  we  say  the  law  of  Gravi- 
tation is  a  fact,  meaning  that  it  is  real,  or  verifiable  by  observa- 
tions or  experiments. 

§  2    Secondary  laws  may  also  be  classified  according  to 
thdr  constancy  into-(i)  the  Invariable  (as  far  as  -^Pfnence 
reaches),    and    (2)    Approximate    Generalisations       Of    the 
Invariable  we  have  given  examples  above.     The  following  are 
Approximate  Generalisations  :  Most  comets  go  round  the  bun 
from   East   to   West ;    Most   metals    are    solid    at    ordinary 
temperatures ;  Most  marsupials  are  Australasian  ;  Most  arctic 
animals  are  white  in  winter ;  Most  cases  of  plague  are  fatal ; 
Most  men  think  first  of  their  own  interests.     Some  of  these 
laws  are  empirical,  as  that '  Most  metals  are  solid  at  ordinary 
temperatures ' :  at  present  no  reason  can  be  given  for  this ;  nor 
do  we  know  why  most  cases  of  plague  are  fatal.     Others,  how- 
ever   are  at  least  partially  derivative,  as   that     Most   arctic 
animals  are  white ' ;  for  this  seems  to  be  due  to  the  advantage 
of  concealment  in  the  snow  ;  whether,  as  with  the  bear,    he 
better  to  surprise  its  prey,  or,  with  the  hare,  to  escape  the 

notice  of  its  enemies. 

But  the  scientific  treatment  of  such  a  proposition  requires 
that  we  should  also  explain  the  exceptions  :  if  '  Most  are  ,  this 
in^phes  that  '  Some  are  not ' ;  why  not,  then  ?  Now,  if  we  can 
give  reasons  for  all  the  exceptions,  the  Approximate  Generali- 
Lion  may  be  converted  into  a  Categorical,  thus  :  All  arctic 
animals  are  white,  unless  (like  the  raven)  they  need  no  conceal- 
ment eitner  to  prey  or  to  escape  ;  or  unless  mutual  recognition 


LAWS   CLASSIFIED 


229 


is  more  important  to  them  than  concealment  (as  with  the 
musk-sheep)'.  The  same  end  of  categorical  statement  may 
be  gained  by  including  the  conditions  on  which  the  pheno- 
menon depends,  thus :  '  All  arctic  animals  to  whom  conceal- 
ment is  of  the  utmost  utility  are  w^hite '. 

When  Statistics  are  obtainable,  it  is  proper  to  convert  an  Approxi- 
mate Generalisation  into  a  proportional  statement  of  the  fact,  thus  : 
instead  of  '  Most  attacks  of  plague  are  fatal ',  we  might  find  that  in  a 
certain  country  70  per  cent,  were  so.  Then,  if  we  found  that  in 
another  country  the  percentage  of  deaths  was  60,  in  another  40,  we 
might  discover,  in  the  different  conditions  of  these  countries,  a  clue  to 
the  high  rate  of  mortality  from  this  disease.  Indeed,  even  if  the 
proportion  of  cases  in  which  two  facts  are  connected  does  not  amount 
to  '  Most ',  yet,  if  any  definite  percentage  is  obtainable,  the  proposition 
has  a  higher  scientific  value  than  a  vague  '  Some  '  :  as  if  we  know  that 
2  per  cent,  of  the  deaths  in  England  are  due  to  suicide,  this  may  be 
compared  with  the  rates  of  suicide  in  other  countries;  from  which 
perhaps  inferences  may  be  drawn  as  to  the  causes  of  suicide. 

In  one  department  of  life,  namely,  Politics,  there  is  a  special 
advantage  in  true  Approximate  Generalisations  amounting  to 
'  Most  cases  '.  The  citizens  of  any  State  are  so  various  in 
character,  enlightenment,  and  conditions  of  life,  that  we  can 
expect  to  find  few  propositions  universally  true  of  them :  so 
that  propositions  true  of  the  majority  must  be  trusted  as  the 
bases  of  legislation.  If  most  men  are  deterred  from  crime  by 
the  fear  of  punishment ;  if  most  men  will  idle  if  they  can 
obtain  support  without  industry ;  if  most  jurymen  will  refuse 
to  convict  of  a  crime  for  which  the  prescribed  penalties  seem 
to  them  too  severe ;  these  are  most  useful  truths,  though  there 
should  be  numerous  exceptions  to  them  all. 

§  3.  Secondary  Laws  can  only  be  trusted  in  '  Adjacent 
Cases ' ;  that  is,  where  the  circumstances  are  similar  to  those 
in  which  the  laws  are  known  to  be  true.  A  Derivative  Law 
will  be  true  wherever  the  forces  concerned  exist  in  the  combi- 
nations upon  which  the  law  depends,  if  there  are  no  counter- 
acting conditions. 

Thus,  that  water  can  be  pumped  to  about  33  feet  at  the  sea-level,  is  a 
derivative  law  on  this  planet:  is  it  true  in  Mars?     That  depends  on 


230      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

whether  there  are  in  Mars  bodies  of  a  liquid  similar  to  our  water; 
whether  there  is  an  atmosphere  there;  and  how  great  its  pressure  is; 
which  will  vary  with  its  height  and  density.  If  there  is  no  atmosphere, 
there  can  be  no  pumping;  or  if  there  is  an  atmosphere  of  less  pressure 
than  ours,  water  such  as  ours  can  only  be  pumped  to  a  less  height 
than  33  feet.  Again,  we  know  that  there  are  arctic  regions  in  Mars; 
if  there  are  also  arctic  animals,  are  they  white?  That  may  depend 
upon  whether  there  are  any  beasts  of  prey.  If  not,  concealment  seems 
to  us  of  no  use. 

An  Empirical  Law,  being  one  whose  conditions  we  do  not 
know,  the  extent  of  its  prevalence  is  still  less  ascertainable. 
Where  it  has  not  been  actually  observed  to  be  true,  we 
cannot  trust  it  unless  the  circumstances,  on  the  whole, 
resemble  so  closely  those  amongst  which  it  has  been  observed, 
that  the  unknown  causes,  whatever  they  may  be,  are  likely  to 
prevail  there.  And,  even  then,  we  cannot  have  much  confidence 
in  it ;  for  there  may  be  unknown  circumstances  which  entirely 
frustrate  the  eftect. 

The   first    naturalist  who  travelled   (say)    from   Singapore  eastward 
by  Sumatra  and  Java,  or  Borneo,  and  found  the  mammalia  there  similar 
to  those  of  Asia,  may  naturally  have  expected  the  same  thing  in  Celebes 
and  Papua;  but.  if  so,  he  was  entirely  disappointed;   for  in  Papua  the 
mammalia  are  marsupials  like  those  of  Australia.     Thus  his  empirical 
law,  'The  mammalia  of  the  Eastern  Archipelago  are  Asiatic,' would 
have  failed  for  no  apparent  reason.     According  to  Mr.  Wallace,  there 
is  a  reason  for  it,  though  such  as  could  only  be  discovered  by  exten- 
sive researches:  namely,  that   the   sea   is   deep   between  Borneo  and 
Celebes,  so  that  they  must  have  been  separated  for  many  ages ;  whereas 
it  is  shallow  from  Borneo  westward  to  Asia,  and  also  southward  from 
Papua  to  Australia;  so  that  these  regions,  respectively,  may  have  been 
recently  united:    and  the  true  law  is  that  similar  mammalia  belong 
to  those  tracts  which  at  comparatively  recent  dates  have  formed  parts 
of  the  same  continents. 

A  considerable  lapse  of  time,  again,  may  make  an  empirical  law  no 
longer  trustworthy ;  for  the  forces  from  whose  combination  it  resulted 
may  have  ceased  to  operate,  or  to  operate  in  the  same  combination ; 
and  since  we  do  not  know  what  those  forces  were,  even  the  knowledge 
that  great  changes  have  taken  place  in  the  meantime  cannot  enable  us, 
after  an  interval,  to  judge  whether  or  not  the  law  still  holds  true.  New 
stars  shine  in  the  sky  and  go  out ;  species  of  plants  and  animals  become 
extinct ;  diseases  die  out  and  fresh  ones  afflict  mankind :  all  these  things 
doubtless  have  their  causes,  but  if  we  do  not  know  what  they  are,  we 


CO-EXISTENCE 


231 


have  no  measure  of  the  effects,  and  cannot  tell  when  or  where  they 
will  happen. 

§  4.  Secondary  Laws,  again,  are  either  of  Succession  or  of 
Co-existence. 

Those  of  Succession  are  either — (i)  of  direct  causation,  as 
that  '  Water  quenches  fire  ',  or  (more  strictly)  that '  Evaporation 
reduces  temperature ' ;  or  (2)  of  the  effect  of  a  remote  cause,  as 
*  Bad  harvests  tend  to  raise  the  price  of  bread ' ;  or  (3)  of  the 
joint  effects  of  the  same  cause,  as  that  '  Night  follows  day ' 
(from  the  revolution  of  the  Earth),  or  the  course  of  the  seasons 
(from  the  inclination  of  the  Earth's  axis). 

Laws  of  Co-existence  are  of  several  classes,  (i)  One  has 
the  generality  of  a  Primary  Law,  though  it  is  proved  only  by 
Agreement,  namely,  *  All  gravitating  bodies  are  inert '.  Others, 
though  less  general  than  this,  are  of  very  extensive  range,  as 
that  *  All  gases  that  are  not  decomposed  by  rise  of  temperature 
have  the  same  rate  of  expansion ' ;  and,  in  Botany,  again, 
that  *  All  monocotyledonous  plants  are  endogenous '.  These 
laws  of  Co-existence  are  concerned  with  the  most  fundamental 
properties  of  bodies. 

(2)  Next  come  laws  of  the  Co-existence  of  those  properties 
which  are  comprised  in   the   definitions   of  Natural    Kinds. 
Mill    distinguished  between  (a)  classes  of  things   that  agree 
among  themselves  and  differ  from  others  only  in  one  or  a 
few  attributes  (such  as  '  red  things ',   '  musical  notes ',   '  car- 
nivorous animals',  soldiers'),  and  (/3)  classes  of  things  that 
agree  among  themselves  and  differ  from  others  in  a  multitude 
of  characters  :  and  the  latter  he  calls  Natural  Kinds.     These 
comprise  the   chemical  elements  and  their   pure  compounds 
(such  as  water,  alcohol,  rock-salt,   chalk),  and  the  species  of 
plants  and  animals.     Clearly,  each  of  these  is  constituted  by 
the  co-existence  or  coinherence  of  a  multitude  of  properties, 
some  of  which  are  selected  as  the  basis  of  their  definitions. 
Thus,  Gold  is  a  metal  of  high  specific  gravity,  high  melting 
point,  low  chemical  affinities,  great  ductility,  yellow  colour,  etc. : 
a  Horse  has  '  a  vertebral  column,  mammae,  a  placental  embryo, 


{ 


232      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 


four  legs,  a  single  well-developed  toe  in  each  foot  provided  with 
a  hoof,  a  bushy  tail,  and  callosities  on  the  inner  sides  of  both 
the  fore  and  the  hind  legs '  (Huxley). 

Since  Darwinism  has  obtained  general  acceptance,  some  logicians 
have  doubted  the  propriety  of  calling  the  organic  species  'Kinds'  on 
the  grounds  that  they  are  not,  as  to  definiteness  and  permanence,  on  a 
par  with  the  chemical  elements  or  such  compounds  as  water  and  rock- 
salt;  that  they  vary  extensively,  and  that  it  is  only  by  the  loss  of 
former  generations  of  animals  that  we  are  able  to  distinguish  species  at 
all.      But  to  this  it  may  be  replied  that  species  (so-called)  are  often 
approximately  constant  for  immense  periods  of  time,  and  may  be  called 
permanent  in  comparison  with  human  generations;  and  that,  although 
the  leading  principles  of  Logic  are  perhaps  eternal  truths,  yet  upon  a 
detail   such   as   this,  the  science  may  condescend  to  recognise  a  dis- 
tinction  if  it   is  good   for   (say)  only    10,000  years.     That   if  former 
generations   of  plants  and  animals  were   not   lost,  all  distinctions   of 
species  would  disappear,  may  be  true ;  but  they  are  lost— for  the  most 
part    beyond    hope   of  recovery;  and   accordingly   the  distinction   of 
species   is   still  recognised;  although   there   are   cases,  chiefly  at   the 
lower  stages  of  organisation,  in  which  so  many  varieties  occur  as  to 
make  adjacent   species  almost  or  quite  indistinguishable.      So  far  as 
species  are  recognised,  then,  they  present  a  complex   co-existence  of 
qualities,  which   is   certainly  a  logical   problem  ;  and,    coming   more 
naturally  under  the  head  of  Natural  Kinds  than  any  other,  they  must 
be  mentioned  in  this  place. 

(3)  There  are,  again,  certain  coincidences  of  qualities  not 
essential  to  any  kind,  and  sometimes  prevailing  amongst  many 
different  kinds  :  such  as  '  Insects  of  nauseous  taste  have  vivid 
(warning)  colours';  '  White  tom-cats  with  blue  eyes  are  deaf; 
*  White  spots  and  patches,  when  they  appear  in  domestic 
animals,  are  most  frequent  on  the  left  side '. 

(4)  Finally,  there  may  be  constancy  of  relative  position,  as 
of  sides  and  angles  in  Geometry;  and  also  among  concrete 
things  (at  least  for  long  periods  of  time),  as  of  the  planetary 
orbits,  the  apparent  positions  of  fixed  stars  in  the  sky,  the 
distribution  of  land  and  water  on  the  globe,  opposite  seasons 
in  opposite  hemispheres. 

All  these  cases  of  Co-existence  (except  the  Geometrical) 
present  the  problem  of  deriving  them  from  Causation ;  for 
there  is  no  general  Law  of  Co-existence  from  which  they  can 


CO-EXISTENCE 


233 


be  derived ;  and,  indeed,  if  we  conceive  of  the  external  world 
as  a  perpetual  redistribution  of  matter  and  energy,  it  follows 
that  the  whole  state  of  Nature  at  any  instant,  and  therefore 
every  Co-existence  included  in  it,  is  due  to  Causation  issuing 
from  some  earlier  distribution  of  matter  and  energy.     Hence, 
indeed,  it  is  not  likely  that  the  problems  of  Co-existence  as  a 
whole  will  ever  be  solved,  since  the  original  distribution   of 
matter  is,  of  course,  unknown.     Still,  starting  with  any  given 
state  of  Nature,  we  may  hope  to  explain  some  of  the   co- 
existences in  any  subsequent  state.     We  do  not,  indeed,  know 
why  weight  always  co-exists  with  inertia,  nor  why  the  chemical ' 
elements   are   what   they   are;    but   it   is   known    that    "the 
properties  of   the    elements   are    functions    of    their    atomic 
weight,"   which   (though,   at   present,   only  an   empirical  law) 
may  be  a  clue  to  some  deeper  explanation.     As  to  plants  and 
animals,  we  know  the  conditions  of  their  generation,  and  can 
trace  a  connection  between  most  of  their  characteristics  and 
the  conditions  of  their  life  :  as  that  teeth  and  stomach  vary 
with  their  food,  and  that  their  colour  generally  varies  with  their 
habitat. 

Geometrical  Co-existence,  when  it  is  not  a  matter  of 
definition  (as  '  a  square  is  a  rectangle  with  four  equal  sides  '), 
is  deduced  from  the  Definitions  and  Axioms :  as  when  it  is 
shown  that  in  triangles  the  greater  side  is  opposite  the  greater 
angle.  The  deductions  of  theorems  or  secondary  laws,  in 
Geometry  is  a  type  of  what  is  desirable  in  the  Physical 
Sciences :  the  demonstration,  namely,  that  all  the  connections 
of  phenomena,  whether  successive  or  co-existent,  are  conse- 
quences of  the  redistribution  of  matter  and  energy  according 
to  the  principle  of  Causation. 

Coincidences  of  Co-existence  (Group  (3)  )  may  sometimes 
be  deduced  and  sometimes  not.  That  '  nauseous  insects  have 
vivid  coloration '  comes  under  the  general  law  of  '  protective 
coloration';  as  they  are  easily  recognised  and  therefore 
avoided  by  insectivorous  birds  and  other  animals.  But  why 
white  tom-cats  with  blue  eyes  should  be  deaf,  is  (I  believe) 


234      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

unknown.  When  Co-existences  cannot  be  derived  from 
Causation,  they  can  only  be  proved  by  collecting  examples 
and  trusting  vaguely  to  the  Uniformity  of  Nature.  If  no 
exceptions  are  found,  we  have  an  empirical  law  of  considerable 
probability  within  the  range  of  our  exploration.  If  exceptions 
occur,  we  have  at  most  an  Approximate  Generalisation,  as  that 
*  Most  metals  are  whitish ',  or  '  Most  domestic  cats  are 
tabbies'  (but  this  is  probably  the  ancestral  colouring).  We 
may  then  resort  to  statistics  for  greater  definiteness,  and  find 
that  in  Hampshire  (say)  ^o  per  cent,  of  the  domestic  cats  are 
tabby. 

§  5.  Scientific  explanation  consists  in  discovering,  deducing, 
and  assimilating  the  laws  of  phenomena.  In  the  ordinary  use 
of  the  word,  explanation  means  the  satisfying  a  man's  under- 
standmg;  and  what  may  serve  this  purpose  depends  partly 
upon  the  natural  soundness  of  his  understanding,  and  partly 
on  his  education. 

Generally,  what  we  are  accustomed  to  seems  to  need  no  explanation, 
unless  our  curiosity  is  particularly  directed  to  it.  That  boys  climb 
trees  and  throw  stones,  and  that  men  go  fox-hunting,  may  easily  pass 
for  matters  of  course.  If  any  one  is  so  exacting  as  to  ask  the  reason, 
there  is  a  ready  answer  in  the  'need  of  exercise.'  On  reflection,  how- 
ever, this  will  not  explain  the  peculiar  zest  of  those  exercises,  which  is 
something  quite  different  from  our  feelings  whilst  swinging  dumb-bells 
or  tramping  the  highway.  Others,  more  sophisticated,  tell  us  that  the 
civilised  individual  retains  in  his  nature  the  instincts  of  his  remote 
ancestors,  and  that  these  assert  themselves  at  stages  of  his  growth 
corresponding  with  ancestral  periods  of  culture  or  savagery:  so  that  if 
we  delight  to  climb  trees,  throw  stones,  and  hunt,  it  is  because  our 
forefathers  once  lived  in  trees,  had  no  missiles  but  stones,  and  depended 
for  a  livelihood  upon  killing  something.  To  some  of  us,  again,  this 
seems  an  explanation  ;  to  others  it  merely  gives  annoyance,  as  a  super- 
fluous hypothesis,  the  fruit  of  a  wanton  imagination  and  too  much 
leisure. 

However,  what  we  are  not  accustomed  to  immediately  excites  curio- 
sity. If  it  were  exceptional  to  climb  trees,  throw  stones,  ride  after 
foxes,  whoever  did  such  things  would  be  viewed  with  suspicion.  An 
eclipse,  a  shooting  star,  a  solitary  boulder  on  the  heath,  a  strange 
animal,  a  Chinaman  in  the  street,  call  for  explanation;  and  among 
some  nations,  eclipses  have  been  explained  by  supposing  a  dragon  to 


EXPLANATION 


235 


devour  the  sun  or  moon;  solitary  boulders,  as  the  missiles  of  a  giant; 
and  so  on.     Such  explanations,  plainly,  are  attempts  to  regard  rare 
phenomena  as  similar  to  others  that  are  better  known;  a  snake  havmg 
been  seen  to  swallow  a  rabbit,  a  bigger  one  may  swallow  the  sun^  a 
gfant  is  supposed  to  bear  much  the  same  relation  to  a  boulder  as  a  boy 
does  to  ha  fa  brick.     When  any  very  common  thmg  seems  to  need  no 
explanation,  it  is  because  the  several  instances  of  its  occurrence  are  a 
suflicient  basis  of  assimilation  to  satisfy  most  of  us.     Still,  ^'^ ^'^^^^^ 
for   such   a  thing  is  demanded,  the  commonest  answer  has  the  s^me 
implication,  namely,  that   assimilation  or  classification  is  ^J-^^^^ 
reason  for  it.     Thus,  if  climbing  trees  is  referred  to  the  need  of  exer 
cise.  it  is  assimilated  to  running,  rowing,  etc. ;  if  the  customs  of  a  savage 
tribe  are  referred  to  the  command  of  its  gods,  they  are  assimilated  to 
those  things  that  are  done  at  the  command  of  chieftains. 

Explanation,  then,  is  the  finding  of  resemblance  between 
the  phenomenon  in  question  and  other  phenomena.  In 
Mathematics,  the  explanation  of  a  theorem  is  the  same  as  its 
proof,  and  consists  in  showing  that  it  repeats,  under  different 
conditions,  the  definitions  and  axioms  already  assumed  and  the 
theorems  already  demonstrated. 

In  Concrete  Sciences,  to  discover  the  cause  of  a  pheno- 
menon is  to  explain  it;  because  a  cause  is  an  invariable 
antecedent,  and  therefore  reminds  us  of,  or  enables  us  to 
conceive,  an  indefinite  number  of  cases  similar  to  the  present 
one  wherever  the  cause  exists ;  and,  as  we  have  seen  that  the 
discovery  of  the  laws  of  nature  is  essentially  the  discovery  of 
causes,  the  discovery  of  laws  is  scientific  explanation. 

The  discovery  of  quantitative  laws  is  especially  satisfactory, 
because  it  not  only  explains  why  an  event  happens  at  all,  but 
why  it  happens  just  in  this  direction,  degree,  or  amount ;  so 
that  (the  only  likeness  between  quantities,  as  such,  being 
equality),  the  cause  is  shown  to  be  equal  not  only  to  other  causes 
but  to  its  own  effect ;  wherefore,  whether  the  conservation  of 
matter  and  energy  be  universally  true  or  not,  it  must  sciU 
be  an  universal  postulate  of  scientific  explanation. 

The  mere  discovery  of  an  empirical  law  of  co-existence,  as 
that  'white  tom-cats  with  blue  eyes  are  deaf,  is  indeed 
something  better  than  an  isolated  fact :  every  general  propo- 


236      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

sition  relieves  the  mind  of  a  load  of  facts ;  and,  for  many 

people,  to  be  able  to  say — '  It  is  alwa\  s  so  ' — may  be  enough  ; 

but  for  scientific  explanation  we  require  to  know  the  reason  of 

it,  that  is,  the  cause.     Still,  if  asked  to  explain  an  Axiom,  we 

can  only  say,  '  It  is  always  so  '. 

§  6.  There  are  three  modes  of  scientific  explanation  :  First, 

the  analysis  of  a  phenomenon  into  the  laws  of  its  causes. 

The  pumping  of  water  implies  (i)  pressure  of  the  air,  (2)  distribution 
of  pressure  in  a  liquid,  (3)  that  motion  takes  the  direction  of  least  resis- 
tance. Similarly,  that  thunder  follows  forked  lightning,  and  that  the 
report  of  a  gun  follows  the  flash,  are  resolvable  into  (i)  the  discharge 
of  electricity,  or  the  explosion  of  gunpowder;  (2)  distance  of  the  observer 
from  the  event;  (3)  that  light  travels  faster  than  sound.  The  planetary 
orbits  are  analysable  into  the  tendency  of  planets  to  fall  into  the  sun, 
and  their  tendency  to  travel  in  a  straight  line.  When  this  conception 
is  helped  out  by  swinging  a  ball  round  by  a  string,  and  then  letting  it 
go,  to  show  what  would  happen  to  the  earth  if  gravitation  ceased,  we 
see  how  the  recognition  of  resemblance  lies  at  the  bottom  of  ex- 
planation. 

Secondly,  the  discovery  of  steps  of  causation  between  a 
cause  and  its  remote  effects ;  the  interpolation  and  con- 
catenation of  causes. 

The  maxim  '  No  cats  no  clover  '  is  explained  by  assigning  the  inter- 
mediate steps  in  the  following  series  ;  that  the  fructification  of  red 
clover  depends  on  the  visits  of  humble-bees,  who  scatter  the  pollen  in 
seeking  honey ;  that  if  field-mice  are  numerous  they  destroy  the 
humble-bees'  nests  ;  and  that  (owls  and  weasels  being  exterminated  by 
game-keepers)  the  destruction  of  field-mice  depends  upon  the  supply  of 
cats;  which,  therefore,  are  a  remote  condition  of  the  clover  crop. 
Again,  the  communication  of  thought  by  speech  is  an  example  of  some- 
thing so  common  that  it  seems  to  need  no  explanation ;  yet  to  explain  it 
is  a  long  story.  A  thought  in  one  man's  mind  is  the  remote  cause  of  a 
similar  thought  in  another's:  Here  we  have  (i)  a  thought  associated 
with  mental  words;  {2)  a  connection  between  these  thoughts  and  some 
tracts  of  the  brain ;  (3)  a  connection  between  these  tracts  of  the  brain 
and  the  muscles  of  the  larynx,  the  tongue  and  the  lips  ;  (4)  movements 
of  the  chest,  larynx  and  mouth,  propelling  and  modifying  waves  of  air ; 
(5)  the  impinging  of  these  air-waves  upon  another  man's  ear,  and  by  a 
complex  mechanism  exciting  the  aural  nerve;  (6)  the  transfer  of  this 
excitation  to  certain  tracts  of  his  brain ;  (7)  a  connection  there  with 
sounds  of  words  and  their  associated  thoughts.  If  one  of  these  links 
fail,  there  is  no  communication. 


EXPLANATION 


237 


Thirdly,  the  Subsumption  of  several  laws  under  one  more 
general  expression. 

Thus  the  tendency  of  bodies  to  fall  to  the  Earth  and  the  tendency  of 
the  Earth  itself  (with  the  other  planets)  to  fall  into  the  Sun,  are  sub- 
sumed under  the  general  law  that  'All  matter  gravitates.'  The  same 
law  subsumes  the  movements  of  the  tide.  By  means  of  the  notion  of 
specific  gravity,  it  includes  '  levitation,'  or  the  actual  rismg  of  some 
bodies,  as  of  corks  in  water,  of  balloons,  or  flames  in  the  air ;  the  fact 
being  that  these  things  do  not  tend  to  rise,  but  to  fall  like  everything 
else ;  only  as  the  water  or  air  weighs  more  in  proportion  to  its  volume 
than  corks  or  balloons,  the  latter  are  pushed  up. 

This  process  of  Subsumption  bears  the  same  relation  to  Secondary 
Laws,  that  these  do  to  particular  facts.  The  generalisation  of  many 
particular  facts  (that  is.  a  statement  of  that  in  which  they  agree)  is  a 
law  and  the  generalisation  of  these  laws  (that  is,  again,  a  statement  of 
that  in  which  they  agree)  is  a  higher  law ;  and  this  process,  upwards  or 
downwards,  is  essentially  the  course  of  scientific  progress.  The  per- 
fecting of  any  science  consists  in  comprehending  more  and  more  of  the 
facts  within  its  province,  and  in  showing  that  they  all  exemplify  a 
smaller  and  smaller  number  of  principles,  which  express  their  most 
profound  resemblances. 

It  can  easily  be  shown  that  these  three  modes  of  explanation 
all  consist  in  generalising  or  assimilating  the  phenomena.  The 
pressure  of  the  air,  of  a  liquid,  and  motion  in  the  direction  of 
least  resistance,  are  all  commoner  facts  than  pumping ;  that 
light  travels  faster  than  sound  is  a  commoner  fact  than  a 
thunder-storm  or  gun-firing.  Each  of  the  laws-^  Cats  kill 
mice,'  'Mice  destroy  humble-bees'  nests,'  'Humble-bees 
fructify  red  clover  '—is  wider  and  expresses  the  resemblance 
of  more  numerous  cases  than  the  law  that  '  Clover  depends 
on  cats';  because  each  of  them  is  less  subject  to  further 
conditions.  Similarly,  every  step  in  the  communication  of 
thought  by  language  is  less  conditional,  and  therefore  more 
general,  than  the  completion  of  the  process. 

In  all  the  above  cases,  again,  each  law  into  which  the 
phenomenon  (whether  pumping  or  conversation)  is  resolved, 
suggests  a  host  of  related  resemblances :  as  the  moditymg  of 
air-waves  by  the  larynx  and  lips  suggests  the  various  devices 


238      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

by   which   the   strings   and   orifices   of    musical    instruments 
modify  the  character  of  notes. 

As  for  Subsumption  (case  (3)),  it  consists  entirely  in 
proving  the  existence  of  an  essential  similarity  between  things 
in  which  it  was  formerly  not  observed:  as  that  the  gyrations 
of  the  moon,  the  M\  of  apples,  and  the  flotation  of  bubbles 
are  all  examples  of  gravitation  :  or  that  the  purifying  of  the 
blood  by  breathing,  the  burning  of  a  candle,  and  the  rustmg 
of  iron  are  all  cases  of  oxidation  :  or  that  the  colouring  of  the 
underside  of  a  red-admiral's  wings,  the  spots  of  the  giraffe,  the 
shape  of  a  stick-caterpillar,  the  transparency  of  deep-sea 
animals,  and  coundess  other  cases,  though  superficially  so 
different,  agree  in  this,  that  they  conceal  and  thereby  protect 

the  organism. 

Not  any  sort  of  likeness,  however,  suffices  for  scientific 
explanation:  it  must  be  'fundamental';  or  (as  this  is  a 
vague  expression)  we  may  say  that  the  only  satisfactory 
explanation  of  concrete  things  or  events,  is  to  discover  their 
likeness  to  others  in  respect  of  Causation.  Hence  attempts 
to  help  the  understanding  by  familiar  comparisons  are  often 
worse  than  useless.  Any  of  the  above  examples  will  show 
that  explanation,  instead  of  making  a  phenomenon  seem 
familiar,  puts  (as  the  saying  is)  'quite  a  new  face  upon  it.' 
The  proneness  to  substitute  familiarisation  for  radical  explana- 
tion, is  the  easily  besetting  sin  of  human  understanding  :  the 
most  plausible  of  fallacies,  the  most  attractive,  the  most  difficult 
to  avoid  even  when  we  are  on  our  guard  against  it. 

§  7.  The  explanation  of  Nature  (if  it  be  admitted  to  consist 
in  generalisation,  or  the  discovery  of  resemblance  amidst 
differences)  can  never  be  completed.  For— (i)  there  are  (as 
Mill  says)  facts,  namely,  fundamental  states  or  processes  of 
consciousness,  which  are  distinct ;  in  other  words,  they  do  not 
resemble  one  another,  and  therefore  cannot  be  generalised 
or  subsumed  under  one  explanation.  Colour,  heat,  smell, 
sound,  touch,  pleasure  and  pain,  are  so  different  that  there  is 
one  group  of  conditions  to  be  sought  for  each ;  and  the  laws 


EXPLANATION 


239 


of  these  conditions  cannot  be  subsumed  under  a  more  general 
one  without  leaving  out  the  very  facts  to  be  explained.  A 
general  condition  of  sensation,  such  as  the  stimulating  of  the 
sensory  organs  of  a  living  animal,  gives  no  account  of  the 
s/>ecia/  characters  of  colour,  smell,  e/c\ ;  which  are,  however,  the 
phenomena  in  question  :  and  each  of  them  has  its  own  law. 

(2)  When  physical  science  is  treated  objectively  (that  is, 
with  as  little  reference  as  possible  to  the  fact  that  all  pheno- 
mena are  only  known  in  relation  to  the  human  mind),  colour, 
heat,  smell,  sound  (considered  as  sensations)  are  neglected, 
and  attention  is  fixed  upon  certain  of  their  conditions  :  Ex- 
tension, Figure,  Resistance,  Weight,  Motion,  with  their 
derivatives.  Density,  Elasticity,  eU.  These  are  called  the 
Primary  Qualities  of  Matter;  and  it  is  assumed  that  they 
belong  to  matter  by  itself,  whether  we  look  on  or  not :  whilst 
colour,  heat,  sound,  etc.,  are  called  Secondary  Qualities,  as 
depending  entirely  upon  the  reaction  of  some  conscious 
animal.  From  this  point  of  view,  the  world  is  considered 
in  the  abstract,  as  a  perpetual  redistribution  of  matter  and 

energy. 

But,  not  to  dwell  upon  the  difficulty  (which  may  be 
temporary)  of  reducing  the  activities  of  life  and  chemistry 
to  mechanical  principles— even  if  this  were  done,  complete 
explanation  could  not  be  attained.  For— («)  as  explanation  is 
the  discovery  of  causes,  we  no  sooner  succeed  in  assigning  the 
causes  of  the  present  state  of  the  world  than  we  have  to  inquire 
into  the  causes  of  those  causes,  and  again  the  still  earlier 
causes,  and  so  on  to  infinity.  But,  this  being  impossible,  we 
must  be  content,  wherever  we  stop,  to  contemplate  the 
uncaused,  that  is,  the  unexplained ;  and  then  all  that  follows 
is  really  unexplained. 

Besides  this  difficulty,  however,  there  is  another  that 
prevents  the  perfecting  of  any  theory  of  the  abstract  material 
world,  namely  (<^),  that  it  involves  more  than  one  first  principle. 
For  we  have  seen  that  the  Uniformity  of  Nature  is  not  really  a 
principle,  but  a  merely  nominal  generalisation,  since  it  cannot 


240      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


be  definitely  stated ;  and,  therefore,  the  principles  of  Contra- 
diction, Mediate  Equality,  and  Causation  remain  incapable  of 
subsumption  ;  nor  can  any  one  of  them  be  reduced  to  another  : 
so  that  they  remain  unexplained. 

(3)  Another  b.ir  to  explanation  lies  in  the  infinite  character 
of  every  particular  fact ;  so  that  we  may  know  the  laws  of 
many  of  its  properties  and  yet  come  far  short  of  understanding 
it  as  a  whole.  A  lump  of  sandstone  in  the  road :  we  may 
know  a  good  deal  about  its  specific  gravity,  temperature, 
chemical  composition,  geological  conditions  ;  but  if  we  inquire 
the  causes  of  the  particular  modifications  it  exhibits  of  these 
properties,  and  further  why  it  is  just  so  big,  containing  so 
many  molecules,  neither  more  nor  less,  disposed  in  just  such 
relations  to  one  another  as  to  give  it  this  particular  figure,  why 
it  lies  exactly  there  rather  than  a  yard  off,  and  so  forth,  we 
shall  get  no  explanation  of  all  this.  The  causes  determining 
each  particular  phenomenon  are  infinite,  and  can  never  be 
computed  ;  and,  therefore,  it  can  never  be  fully  explained. 

§  8.  Analogy   is    a   kind    of   probable   proof    based    upon 

imperfect    similarity   (as   the    best    that    can    be    discovered) 

between    the   data   of   comparison    and    the   subject   of    our 

inference.     Like   Deduction  and   Induction,  it  assumes  that 

things  which  are  alike  in    some    respects   are   also  alike    in 

others ;  but  it  differs  from  them  in  not  appealing  to  a  definite 

general  law  assigning  the  essential  points  of  resemblance  upon 

which  the  argument  relies.     In  Deductive  proof,  this  is  done 

by  the  major  premise  of  every  syllogism  :    if  the  major  says 

that  *  All  fat  men  are  humourists ',  and  we  can  establish  the 

minor,    '  X    is   a   fat    man ',    we    have    secured   the   essential 

resemblance  that  carries  the  conclusion.     In   Induction,  the 

Law  of  Causation  and  its  representatives,  the  Canons,  serve 

the  same  purpose,  specifying  the  essential   marks  of  a  cause. 

But,  in  Analogy,  the  resemblance  relied  on  cannot  be  stated 

categorically. 

If  we  argue  that  Mars  is  inhabited  because  it  resembles  the  datum, 
our  Earth,  (i)  in  being  a  planet,  (2)  neither  too  hot  nor  too  cold  for 


ANALOGY 


4.1 


life,  (3)  having  an  atmosphere,  (4)  sea  and  land,  etc.,  we  are  not  pre- 
pared to  say  that  '  All  planets  having  these  characteristics  are  inhabited.' 
It  is,  therefore,  not  a  deduction  ;  and  since  we  do  not  know  the  original 
causes  of  life  on  the  Earth,  we  certainly  cannot  show  by  induction  that 
adequate  causes  exist  in  Mars.  We  rely,  then,  upon  some  such  vague 
notion  of  Uniformity  as  that  '  Things  alike  in  some  points  are  alike  in 
others ' ;  which,  plainly,  is  either  false  or  nugatory. 

The  cogency  of  any  proof  depends  upon  the  character  and 

definiteness  of  the  likeness  which  one  phenomenon   bears    to 

another ;  but  Analogy  trusts  to  the  general  quantity  of  likeness 

between  them,  in  ignorance  of  what  may  be  the  really  important 

likeness. 

If,  having  tried  with  a  stone,  an  apple,  a  bullet,  etc.,  we  find  that  they 
all  break  an  ordinary  window,  and  thence  infer  that  a  cricket  ball  will 
do  so,  we  do  not  reason  by  Analogy,  but  make  instinctively  a  deductive 
extension  of  an  induction,  merely  omitting  the  explicit  generalisation, 
'All  missiles  of  a  certain  weight,  size  and  solidity  break  windows.' 
But  if,  knowing  nothing  of  snakes  except  that  the  viper  is  venomous,  a 
child  runs  away  from  a  grass-snake,  he  argues  by  Analogy;  and,  though 
his  conduct  is  prudentially  justifiable,  his  inference  is  wrong:  for  there 
is  no  law  that  'A.ll  snakes  are  venomous,'  but  only  that  those  are 
venomous  that  have  a  certain  structure  of  fang ;  a  point  which  he  did 
not  stay  to  examine.  . 

Analogical  argument,  therefore,  is  only  probable,  and  that 
in  various  degrees. 

(i)  The  greater  the  number  and  importance  of  the  points 
of  agreement,  the  more  probable  is  the  inference.  (2)  The 
greater  the  number  and  importance  of  the  points  of  difference, 
the  less  probable  is  the  inference.  (3)  The  greater  the  number 
of  unknown  properties  in  the  subject  of  our  argument,  the 
less  the  value  of  any  inference  from  those  that  we  do  know. 
Of  course  the  number  of  unknown  properties  can  itself  be 
estimated  only  by  Analogy.  In  the  case  of  Mars,  they  are 
probably  very  numerous ;  and  the  prevalent  assumption  that 
there  are  intelligent  beings  in  that  planet,  seems  to  rest  less 
upon  probability  than  on  a  curiously  imaginative  extension  of 
the  gregarious  sentiment,  and  a  hope  that  there  may  be 
conversable  and  '  clubable '  souls  nearer  than  the  Dog-star. 


CHAPTER  XX 


PROBABILITY 


§  I.  Chance  was  once  believed  to  be  a  distinct  power  in  the 
world,  disturbing  the  regularity  of  Nature  ;  though,  accoiding 
to  Aristotle,  it  was  only  operative  in  occurrences  below  the 
sphere  of  the  moon.  As,  however,  it  is  now  admitted  that 
every  event  in  the  world  is  due  to  some  cause,  if  we  can  only 
trace  the  connection,  whilst  nevertheless  the  notion  of  Chance 
is  still  useful  when  rightly  conceived,  we  have  to  find  some 
other  ground  for  it  than  that  of  a  spontaneous  capricious  force 
inherent  in  things. 

Every  event  is  a  result  of  causes  :  but  the  multitude  of  forces 
and  the  variety  of  collocations  beir^  immeasurably  great,  the 
overwhelming  majority  of  events  occurring  about  the  same  time 
are  only  related  by  Causation  so  remotely  that  the  connection 
cannot  be  followed.  Whilst  my  pen  moves  along  the  paper,  a  cab 
rattles  down  the  street,  bells  in  the  neighbouring  steeple  chime 
the  quarter,  a  girl  in  the  next  house  is  practising  her  scales, 
and  throughout  the  world  innumerable  events  are  happening 
which  may  never  happen  together  again,  so  that  should  one  of 
them  recur,  we  have  no  reason  to  expect  any  of  the  others. 
This  is  Chance,  or  chance  coincidence.     1  he  word  coincidence 
is  vulgarly  used  only  for  the  inexplicable  concurrence  of  in- 
teresting events — "  quite  a  coincidence  !  " 

On  the  other  hand,  many  things  are  now  happening  together 
or  coinciding,  that  will  do  so,  for  assignable  reasons,  again  and 
again ;  thousands  of  men  are  leaving  the  City,  who  leave  at 
the  same  hour  five  days  a  week.     But  this  is  not  chance ;  it  is 


PROBABILITY 


243 


causal  coincidence  due  to  the  custom  of  business  m  this  country, 
as  determined  by  our  latitude  and  longitude  and  other  circum- 
stances No  doubt  the  above  chance  coincidences— writing, 
cab-rattling,  chimes,  scales,  ./..-are  causally  connected  at  some 
point  of  past  time.  They  were  predetermined  by  the  condition 
of  the  world  ten  minutes  ago ;  and  that  was  due  to  earlier  con- 
ditions, one  behind  the  other,  even  to  the  formation  of  the 
planet  But  whatever  connection  there  may  have  been,  we 
have  no  such  knowledge  of  it  as  to  be  able  to  deduce  the 
coincidence,  or  calculate  its  recurrence.  Hence  Chance  is 
defined  by  Mill  to  be :  Coincidence  giving  no  ground  to  inter 

uniformity. 

However,  in  fact,  some  chance  coincidences  do  recur  ac- 
cording to  laws  of  their  own  :  I  say  some,  but  it  may  be  all.     If 
the  world  is  finite,  the  possible  combinations  of  its  elements 
are  exhaustible ;  and,  in  time,  whatever  conditions  of  the  world 
have  concurred  will  concur  again,  and  in  the  same  relation  to 
former  conditions.     This  writing,  that  cab,  those  chimes,  those 
scales  will  coincide  again  :  the  Argonautic  expedition,  and  the 
Trojan  war,  and  all  our  other  troubles  will  be  renewed.     But, 
to  avoid  melancholy,  let  us  consider  some  more  manageable 
instance,  such  as  the  throwing  of  dice.     Every  one  who  has 
played  much  with  dice  knows  (so  I  am  told)  that  double  sixes 
are   sometimes   thrown,  and   sometimes   double   aces.     Such 
coincidences  do  not  happen  once  and  only  once ;  they  occur 
again  and  again,  and  a  great  number  of  trials  will  show  that 
though  their  recurrence  has  not  the  regularity  of  cause  and 
effect,  it  yet  has  a  law  of  its  own,  namely-a  tendency  to  average 
regularity.     In  10,000  throws  there  will  be  some  number  of 
double   sixes;    and   the    greater   the  number  of  throws,  the 
more  closely  will  the  average  recurrence  of  double  sixes,  or 
double   aces,  approximate   to  one  in  thirty-six      Such  a  law 
of  average  recurrence  is   the  basis   of  Probability.     Chance 
being  the  fact  of  coincidence  without  assignable  cause.  Proba- 
bility is  expectation  based  on  the  average  frequency  of  its 
happening. 


244      LOGIC:    DEDUCTIVE    AND   INDUCTIVE 

§  2.  Probability  is  an  ambiguous  term.  Uusually,  when  we 
say  that  an  event  is  '  probable,'  we  mean  that  it  is  more  likely 
than  not  to  happen.  But,  scientifically,  an  event  is  probable 
if  our  expectation  of  its  occurrence  is  less  than  certainty,  as 
long  as  the  event  is  not  impossible.  Probability  thus  conceived 
is  represented  by  a  fraction.  Taking  i  to  stand  for  certainty, 
and  o  for  impossibility,  probability  may  be  VWo'  ^^  ioVo>  ^^ 
(generally)  i.  The  denominator,  of  course,  represents  the 
number  of  times  that  an  event  happens,  and  the  numerator  the 
number  of  times  that  it  coincides  with  another  event.  In 
throwing  a  die,  the  probability  of  ace  turning  up  is  expressed 
by  putting  the  number  of  throws  for  the  denominator  and  the 
number  of  times  that  ace  is  thrown  for  the  numerator  ;  and  we 
may  assume  that  the  more  trials  we  make  the  nearer  will  the 
resulting  fraction  approximate  to  J. 

Instead  of  speaking  of  the  'throwing  of  the  die'  and  its 
'  turning  up  ace '  as  two  events,  the  former  is  often  called  '  the 
event'  and  the  latter  'the  way  of  its  happening.'  And  these 
expressions  may  easily  be  extended  to  cover  relations  of  distinct 
events ;  as  when  two  men  shoot  at  a  mark  and  we  desire  to 
represent  the  probability  of  both  hitting  the  bull's  eye  together, 
each  shot  may  count  as  an  event  (denominator)  and  the  coinci- 
dence of  '  bull's-eyes  '  as  the  way  of  its  happening  (numerator). 

It  is  also  common  to  speak  of  probability  as  a  proportion. 
If  the  fraction  expressing  the  probability  of  ace  being  cast  is  ^, 
the  proportion  of  cases  in  which  it  happens  is  i  to  5 ;  or  (as  it 
is,  perhaps,  still  more  commonly  put)  '  the  chances  are  5  to  i 

against  it.' 

§  3.  As  to  the  grounds  of  probability  opinions  differ. 
According  to  one  view  the  ground  is  subjective:  probability 
depends,  it  is  said,  upon  the  quantity  of  our  Belief  in  the 
happening  of  a  certain  event,  or  of  its  happening  in  a  particular 
way.  According  to  the  other  view  the  ground  is  objective,  and, 
in  fact,  is  nothing  else  than  experience,  which  is  most  trust- 
worthy when  carefully  expressed  in  statistics. 

To  the  subjective  view  it  rnay  be  objected,  (a)  that  Belief 


PROBABILITY 


245 


cannot  by  itself  be  satisfactorily  measured.  Surely,  no  one 
will  maintain  that  Belief,  merely  as  a  state  of  mind,  always  has 
a  definite  numerical  value  of  which  one  is  conscious,  as  yjo  ^^ 
j\.  Let  anybody  mix  a  number  of  letters  in  a  bag,  knowing 
nothing  of  them  except  that  one  of  them  is  X,  and  then  draw 
them  one  by  one,  endeavouring  each  time  to  estimate  the  value 
oi  his  belief  that  the  next  will  be  X ;  can  he  say  that  his  belief 
in  the  drawing  of  X  regularly  increases  as  the  number  of  letters 

Ipft  decreases  ? 

If  not,  we  see  that  {d)  Belief  does  not  uniformly  correspond 
with  the  state  of  the  facts.     If  in  such  a  trial  as  proposed  above, 
we  really  wish  to  draw  X  (as  in  looking  for  somethmg  in  a 
number  of  boxes),  how  common  it  is  after  a  fewfaimres  to  feel 
quite  hopeless  and  to  say  :  "  Oh,  of  course  it  will  be  in  the  last." 
For  belief  is  subject  to  hope  and  fear,  temperament,  passion 
and  prejudice,  and  not  merely  to  rational  considerations.     And 
it  is  useless  to  appeal  to  '  the  Wise  Man,'  the  purely  rational 
judge  of  probability,  unless  he  is  producible.     Or,  if  it  be  said 
that  belief  is  a  short  cut  to  the  evaluation  of  experience,  be- 
cause in  fact  it  is  the  resultant  of  all  past  experience,  we  may 
reply  that  this  is  not  true.      For  everybody  knows  that  one 
striking  experience,  or  two  or  three  recent  ones,  will  immensely 
outweigh  a  great  number  of  faint  or  remote  experiences.     More- 
over, the  experience  of  two  men  may  be  practically  equal,  whilst 
their  beliefs  upon  any  question  greatly  differ.     Any  two  English- 
men have  about  the  same  experience,  personal  and  ancestral, 
of  the  weather  ;  yet  their  beliefs  in  the  saw  that  '  if  it  ram  on 
St.  Swithin's  Day  it  will  rain  for  forty  days  after,'  may  differ  as 
confident  expectation  and  sheer  scepticism.     Upon  which  of 
these  beliefs  shall  we  ground  the  probability  of  forty  days  rain? 
But  {c),  at  any  rate,  if  Probability  is  to  be  connected  with 
Inductive  Logic,  it  ought  surely  to  rest  upon  the  same,  ground, 
namely— Observation.     Induction,  in  any  particular  case,  is 
not  content  with  beliefs  or  opinions,  but   aims   at   probing, 
testing,  verifying  or  correcting  them  by  appealing  to  the  facts ; 
and  Probability  has  the  same  object  and  the  same  basis. 


246      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 


There  are,  indeed,  cases  in  which  the  conditions  of  an  event 
are  supposed  to  be  mathematically  predetermined,  as  in  tossing 
a  penny,  tiirowing  dice,  dealing  cards.  In  throwing  a  die,  the 
ways  of  happening  are  six ;  in  tossing  a  penny  only  two,  head 
and  tail :  and  we  usually  assume  that  the  odds  with  a  die  are 
fairly  5  to  i  against  ace,  whilst  with  a  penny  'the  betting  is 
even'  on  head  or  tail.  Still,  this  assumption  rests  upon  another, 
that  the  die  is  perfectly  fair,  or  that  the  head  and  tail  of  a  penny 
are  exactly  alike ;  and  this  is  not  true.  With  an  ordinary  die 
or  penny,  a  very  great  number  of  trials  would,  no  doubt,  give 
an  average  approximating  to  J  or  J  ;  yet  might  always  leave  a 
certain  excess  one  way  or  the  other,  which  would  also  become 
more  definite  as  the  trials  went  on ;  thus  showing  that  the  die 
or  penny  did  not  satisfy  the  mathematical  hypothesis.  Buffon 
is  said  to  have  tossed  a  coin  4040  times,  obtaining  1992  heads 
and  2048  tails ;  a  pupil  of  De  Morgan  tossed  4092  times, 
obtaining  2048  heads  and  2044  tails. 

There  are  other  important  cases  in  which  probability  is 
estimated  and  numerically  expressed,  although  statistical 
evidence  directly  bearing  upon  the  point  in  question  cannot  be 
obtained  ;  as  in  betting  upon  a  race  ;  or  in  the  prices  of  stocks 
and  shares,  which  are  supposed  to  represent  the  probability  of 
their  paying,  or  continuing  to  pay,  a  certain  rate  of  interest. 
But  the  judgment  of  experts  in  such  matters  is  certainly  based 
upon  experience  ]  and  great  pains  are  taken  to  make  the 
evidence  as  definite  as  possible  by  comparing  records  of  speed, 
or  by  financial  estimates  ;  though  something  must  still  be 
allowed  for  reports  of  the  condition  of  horses,  or  of  the  prospects 
of  war,  etc. 

However,  where  statistical  evidence  is  obtainable,  no  one 
dreams  of  preferring  to  estimate  probability  by  the  quantity  of 
his  belief.  Insurance  offices,  dealing  with  fire,  shipwreck, 
death,  accident,  etc.,  prepare  elaborate  statistics  of  these 
events,  and  regulate  their  rates  accordingly.  Apart  from 
statistics,  at  what  rate  ought  the  lives  of  men  aged  40  to  be 
insured,  in  order  to  leave  a  profit  of  5  per  cent,  upon  jQiooo 


PROBABILITY 


247 


payable   at   each    man's   death?      Is    'quantity   of  belief   a 
sufficient  basis  for  doing  this  sum  ? 

§  4.  The  ground   of  probability  is  experience,   then,  and, 
whenever  possible,  statistics  ;  which  are  a  kind  of  inductions. 
It  has  indeed  been  urged  that  induction  is  itself  based  upon 
probability;    that   the   subtlety,    complexity   and    secrecy   of 
nature  are  such,  that  we  are  never  quite  sure  that  we  fully 
know  even  what  we  have  observed  ;  and  that,  as  for  laws,  the 
conditions  of  the  universe  at  large  may  at  any  moment  be 
completely   changed;    so   that   all    imperfect   inductions,    in- 
cluding the  law  of  Causation  itself,  are  only  probable.     But, 
clearly,  this  doctrine  turns  upon  another  ambiguity  in  the  word 
'probable.'     It  may  be  used  in  the  sense  of  Mess  than  abso- 
lutely certain  ' :    and  such  doubtless  is  the  condition  of  all 
human   knowledge,    in    comparison    with   the   comprehensive 
intuition  of  archangels  ;   or  it  may  mean   '  less  than  certain 
according  to  our  standard  of  certainty/  that  is,  in  comparison 
with  the  law  of  Causation  and  its  derivatives. 

We  may  suppose  some  one  to  object  that  "  by  this  relative 
standard  even  empirical  laws  cannot  be  called  '  only  probable ' 
as  long  as  we  '  know  no  exception  to  them ' ;  for  that  is  all  that 
can   be   said   for   the  boasted   law  of  Causation  ;    and  that, 
accordingly,  we   can    frame    no    fraction    to   represent    their 
probability.     That  'all  swans  are  white'  was  at  one  time,  from 
this  point  of  view,  not  probable  but  certain  ;  though  we  now 
know  it  to  be  false.     It  would  have  been  an  indecorum  to  call 
it   only  probable   as   long   as    no    other   coloured   swan  was 
known ;  not  merely  because  the  quantity  of  belief  amounted  to 
certainty,  but  because  the  number  of  events  (seeing  a  swan) 
and  thenumber  of  their  happenings  in  a  certai  n  way  (being 
white)  were  equal,  and  therefore  the  evidence  amounted  to  i 

or  certainty." 

But  we  reply,  that  such  an  empirical  law  is  only  probable, 
and  that  the  estimate  of  its  probability  must  be  based  on  the 
number  of  times  that  similar  laws  have  been  found  liable  to 
exceptions.     White  crows,  though  rare,  are  exceptions  to  the 


248      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


law  that  crows  are  black  ;  and  it  is  not  uncommon  to  find 
allied  varieties  of  animals  differing  in  colour  in  different 
localities.  Had  the  evidence  been  known  and  duly  weighed, 
then,  it  could  never  have  seemed  more  than  probable  that 
'  all  swans  are  white.'  But  what  law,  similar  in  rank  to  the  law 
of  Causation,  presents  any  exceptions  ? 

It  ought  not  to  be  difficult  to  see  that  induction,  humanly 
speaking,  does  not  rest  on  probability  ;  but  that  the  probability 
of  concrete  events  (not  of  mere  mathematical  abstractions  like 
the  falling  of  absolutely  true  dice)  rests  on  induction  and, 
therefore,  on  Causation. 

The  inductive  evidence  underlying  an  estimate  of  probability 
may  be  of  three  kinds  :  (a)  direct  statistics  of  the  events  in 
question ;  as  when  we  find  that,  at  the  age  of  20,  the  average 
expectation  of  life  is  39-40  years.  This  is  an  empirical  law, 
and,  if  we  do  not  know  the  causes  of  any  event,  we  must  be 
content  with  an  empirical  law.  But  (/?)  if  we  do  know  the 
causes  of  an  event,  and  the  causes  which  may  prevent  its 
happening,  and  can  estimate  the  comparative  frequency  of 
their  occurring,  we  may  deduce  the  probability  that  the  effect 
(that  is,  the  event  in  question)  will  occur.  Or  (c)  we  may 
combine  these  two  methods,  verifying  each  by  means  of  the 
other.  Now  either  the  method  (fi)  or  (<?  fortiori)  the  method 
{c)  (both  depending  on  Causation)  is  more  trustworthy  than  the 
method  (a)  by  itself. 

But,  further,  a  merely  empirical  statistical  law  will  only  be 
true  as  long  as  the  causes  influencing  the  event  remain  the 
same.  A  die  may  be  found  to  turn  ace  once  in  six  throws,  on 
the  average,  in  close  accordance  with  mathematical  theory  ; 
but  if  we  load  it  on  that  facet  the  results  will  be  very  different. 
So  it  is  with  the  expectation  of  life,  or  fire,  or  shipwreck.  The 
increased  virulence  of  some  epidemic  such  as  influenza,  an 
outbreak  of  anarchic  incendiarism,  a  moral  epidemic  of  over- 
loading ships,  may  deceive  the  hopes  of  insurance  offices. 
Hence  we  see,  again,  that  probability  depends  upon  causation, 
not  causation  upon  probability. 


PROBABILITY 


249 


§  5      The  nature  of  an  average  supposes  deviations  from  it. 
These  deviations,   or   '  errors,'  conform  to  the   law  that   the 
greater  are  less  frequent  than  the  smaller,  so  that  most  of  the 
events   approximate    to    the    average.       The    calculation    of 
probabilities,  in  fact,  supposes  a  class  or  series  of  mstances  or 
events,    subject   (as    far   as   is   known)    to    somewhat  similar 
conditions,  though    the    conditions   are  not  so  similar  as  to 
result  in  uniformity.     Where  the  more  similar  conditions  pre- 
dominate,  they  produce  average  instances;  where  dissimilar 
conditions  occur,  but  in  such  a  way  as  to  cancel  one  another, 
the  average  again   results  ;    where   unusual  conditions  occur 
without  cancelling,  extraordinary  instances  appear.     Hence  if 
the  average  height  of  a  nation  is  5  ft.  6  in.,  most  men  will  be 
about  that  size ;  men  of  5  ft.  and  6  ft.  will  be  rare,  and  those 
of  4  ft.  6  in.  and  6  ft.  6  in.  rarer  still ;  whilst  limits  to  height 
in  both  directions  seem  to  be  fixed  by  the  nature  of  things. 
Li  casting  a  die,  in  sets  of  six  throws,  ace  will  turn  up  oftener 
once  than  twice  in  each  set  of  throws,  oftener  twice  than  three 
times,  though  it  may  appear  every  time  in  six,  and  even  in 
continuous  sets  of  sixes ;  and,  in  such  a  case,  there  seems  {a 
priori)  to  be  no  necessary  limit  to  the  length  of  sequences 
that  may  occur  in  infinite  trials. 

These  considerations  have  an  important  bearing  upon  the 
interpretation   of  probabilities.     The  average  probability  for 
any  general  class  or  series  of  events  cannot  be  confidently 
applied  to  any  one  instance  or  to  any  special  class  of  instances, 
since  this  one,  or  this  special  class,  may  exhibit  a  striking  error 
or  deviation  ;  it  may,  in  fact,   be  subject  to  special  causes. 
Within  the  class  whose  average  is  first  taken,  and  which  ^is 
described  by  general  characters  as  '  a  man,'  or  '  a  die,'  or  *  a 
rifle  shot,'  there  may  be   special  classes   marked   by   special 
characters  and   determined   by  special  influences.     Statistics 
giving  the  average  for  ^  mankind  '  may  not  be  true  of '  civilised 
men,'  or  any  still  smaller  class  such  as  '  inhabitants  of  U.S.A.' 
Hence  life-insurance  offices  rely  not  merely  on  statistics  of  life 
and  death  in  general,  but  collect  special  evidence  in  respect  of 


250      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

different  ages  and  sexes,  and  make  further  allowance  for 
teetotalism,  inherited  disease,  etc.  Similarly  for  individual 
cases :  the  average  expectation  for  a  class,  whether  general  or 
special,  is  only  applicable  to  any  particular  case  if  that  case  is 
adequately  described  by  the  class  characters.  In  England, 
for  example,  the  average  expectation  of  life  for  males  at  20 
years  of  age  is  3940 ;  but  at  60  it  is  still  i3'i4,  and  at  73  it  is 
7  "07  ;  at  100  it  is  i-6i.  Of  men  20  years  old  those  who  live 
more  or  less  than  39  40  years  are  deviations  or  errors  ;  but 
there  are  a  great  many  of  them.  To  insure  the  life  of  a  single 
man  at  20,  in  the  expectation  of  his  dying  at  60,  would  be  a 
mere  bet,  if  we  had  no  special  knowledge  of  him  ;  the  safety 
of  an  insurance  office  lies  in  having  so  many  clients  that 
opposite  deviations  cancel  one  another  :  the  more  clients  the 
safer  the  business.  It  is  quite  possible  that  a  hundred  men 
aged  20  should  be  insured  in  one  week  and  all  of  them  die 
before  25  :  this  would  bt  ruinous,  if  others  did  not  live  to  be 
80  or  90. 

Not  only  in  such  a  practical  affair  as  insurance,  but  in 
matters  purely  scientific,  the  minute  and  subtle  peculiarities  of 
individuals  have  important  consequences.  Each  man  has  a 
certain  cast  of  mind,  character,  physique,  giving  a  distinctive 
turn  to  all  his  actions  even  when  he  tries  to  be  normal.  In 
every  employment  this  determines  his  Personal  Equation,  or 
average  deviation  from  the  normal.  The  term  Personal 
Equation  is  used  chiefly  in  connection  with  scientific  observa- 
tion, as  in  Astronomy.  Each  observer  is  liable  to  be  a  little 
wrong,  and  this  error  has  to  be  allowed  for  and  his  observations 
corrected  accordingly. 

The  use  of  the  term  *  expectation,'  and  of  examples  drawn 
from  insurance  and  gambling,  is  apt  to  convey  the  notion  that 
probability  relates  entirely  to  future  events  ;  but  if  it  is  based 
on  laws  and  causes  it  can  have  no  reference  to  point  of  time. 
As  long  as  conditions  are  the  same  events  will  be  the  same, 
whether  we  consider  uniformities  or  averages.  We  may  there- 
fore draw  probable  inferences  concerning  the  past  as  well  as 


PROBABILITY 


251 


the  future,  subject  to  the  same  hypothesis,  that  the  causes 
affecting  the  events  in  question  be  the  same  and  similarly 
combined.  On  the  other  hand,  if  we  know  that  conditions 
bearing  on  the  subject  of  investigation,  have  changed  since 
statistics  were  collected,  or  were  different  at  some  time  previous 
to  the  collection  of  evidence,  every  probable  inference  based 
on  those  statistics  must  be  corrected  by  allowing  for  the  altered 
conditions,  whether  we  desire  to  reason  forwards  or  backwards 
in  time. 

§  6    The  rules  for  the  combination  of  probabilities  are  as  follows: 

(1)  If  two  events  or  causes  do  not  concur,  the  probability  of  one  or 
the  other  occurring  is  the  sum  of  the  separate  probabihties.  A  die 
cannot  turn  up  both  ace  and  six;  but  the  probability  in  favour  of  each 
is  \:  therefore,  the  probability  in  favour  of  one  or  the  other  is  J. 
Death  can  hardly  occur  from  both  burning  and  drowning :  if  i  in  1000 
is  burned  and  2  in  1000  are  drowned,  the  probabiUty  of  being  burnt  or 

drowned  is  kh^^- 

(2)  If  two  events  are  independent,  having  neither  connection  nor 
repugnance,  the  probabiUty  of  their  concurring  is  found  by  multiplying 
together  the  separate  probabilities  of  each  occurring. 

If  in  walking  down  a  certain  street  I  meet  A  once  in  four  times,  and 
B  once  in  three  times,  I  ought  (by  mere  chance)  to  meet  both  once  m 
twelve  times:  for  in  twelve  occasions  I  meet  B  four  times;  but  once  m 

four  I  meet  A.  ...         -4. 

This  is  a  very  important  rule  in   scientiEc   investigation,   since  it 
enables  us  to  detect  the  presence  of  causation.     For  if  the  coincidence 
of  two  events  is  more  or  less  frequent  than  it  would  be  if  they  were 
entirely  independent,  there  is  either  connection  or  repugnance  between 
them      If  ^  ^. .  in  walking  down  the  street  I  meet  both  A  and  B  oftener 
than  once  in  twelve  times,  they  may  be  engaged  in  similar  business, 
calling  them  from  their  office*  at  about  the  same  hour.     If  I  meet  them 
both  less  often  than  once  in  twelve  times,   they  may  belong  to  the 
same  office,  where  one  acts  as  a  substitute  for  the  other.     Similarly, 
if  in  a   multitude  of  throws  a  die  turns  six  oftener  than  once   in  six 
times,  it  is  not  a  fair  one:  that  is.  there  is  a  cause  favouring  the  turning 

""  H  of  20.000  people  500  see  apparitions  and  100  have  friends  murdered 
the  chance  of  any  man  having  both  experiences  is  ^Air  i  but  if  each 
lives  on  the  average  300.000  hours,  the  chance  of  both  events  occurring 
in  the  same  hour  is  ^,^^,W^^^-     I^  ^he  two  events  occur  m  the  same 
hour  oftener  than  this,  there  is  more  than  a  chance  coincidence. 

The  more  minute  a  cause  of  connection  or  repugnance  between  events. 


252      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


the  longer  the  series  of  trials  or  instances  necessary  to  bring  out  its 
influence.  The  less  a  die  is  loaded,  the  more  casts  must  be  made  before 
it  can  be  shown  that  a  certain  side  tends  to  recur  oftener  than  once  in 
six. 

{3)  The  rule  for  calculating  the  probability  of  a  dependent  event  is 
clearly  the  same  as  the  above ;  for  the  concurrence  of  two  independent 
events  is  itself  dependent  upon  each  of  them  occurring.  My  meeting 
with  both  A  and  B  in  the  street  is  dependent  on  my  walking  there  and 
on  my  meeting  one  of  them.  Similarly,  if  A  is  sometimes  a  cause  of 
B  (though  liable  to  be  frustrated),  and  B  sometimes  of  C  (C  and  B 
having  no  causes  independent  of  B  and  A  respectively),  the  occurrence 
of  C  is  dependent  on  that  of  B,  and  that  again  on  the  occurrence  of  A. 
Hence  we  may  state  the  rule:  If  two  events  are  dependent  each  on 
another,  so  that  if  one  occur  the  second  may  (or  may  not),  and  if  the 
second  a  third;  whilst  the  third  never  occurs  without  the  second,  nor 
the  second  without  the  first ;  the  probability  that  if  the  first  occur  the 
third  will,  is  found  by  multiplying  together  the  fractions  expressing  the 
probability  that  the  first  is  a  mark  of  the  second  and  the  second  of  the 
third. 

Upon  this  principle  the  value  of  hearsay  evidence  or  tradition 
deteriorates,  and  generally  the  cogency  of  any  argument  based  upon 
the  combination  of  approximate  generalisations  dependent  on  one 
another  or  "  self-infirmative."  If  there  are  two  witnesses,  A  and  B,  of 
whom  A  saw  an  event,  whilst  B  only  heard  A  relate  it  (and  is  therefore 
dependent  on  A),  what  credit  is  due  to  B's  recital  ?  Suppose  the  proba- 
bility of  each  man's  being  correct  as  to  what  he  says  he  saw,  or  heard, 


then  (; 


3  _  9 


^yr)  the  probability  that  B's  story  is  true  is  a  little 


IS    ^ 

more  than  h-  For  if  in  16  attestations  A  is  wrong  4  times,  B  can  only 
be  right  in  f  of  the  remainder,  or  g  times  in  16.  Again,  if  we  have  the 
Approximate  Generalisations,  '  Most  attempts  to  reduce  wages  are  met 
by  strikes,'  and  'Most  strikes  are  successful,'  and  learn,  on  statistical 
inquiry,  that  in  every  hundred  attempts  to  reduce  wages  there  are  80 
strikes,  and  that  70  p.c.  of  the  strikes  are  successful,  then  56  p.c.  of 
attempts  to  reduce  wages  are  unsuccessful. 

Of  course  this  method  of  calculation  cannot  be  quantitatively  applic- 
cable  if  no  statistics  are  obtainable,  as  in  the  testimony  of  witnesses; 
and  even  if  a  numerical  value  could  be  attached  to  the  evidence  of  a 
certain  class  of  witnesses,  it  would  be  absurd  to  assume  it  for  particular 
members  of  the  class  without  taking  account  of  their  education,  interest 
in  the  case,  prejudice,  or  general  capacity.  Still,  the  numerical  illus- 
tration of  the  rapid  deterioration  of  hearsay  evidence,  when  less  than 
quite  veracious,  puts  us  on  our  guard  against  rumour.  To  retail 
rumour  may  be  as  bad  as  to  invent  an  original  lie. 

(4)  If  an  event  may  coincide  with  two  or  more  other  independent 
events,  the  probability  that  they  will  together  be  a  sign  of  it,  is  found 


PROBABILITY 


253 


by  multrplying  together  the   fractions  representing  the  improbability 
that  each  is  a  sign  of  it,  and  subtracting  the  product  from  unity. 

This  is  the  rule  for  estimating  the  cogency  of  cumulative  testimony, 
circumstantial  evidence,  analogical  evidence ;  or,  generally,  for  com- 
bining Approximate  Generalisations  "  self-corroboratively. 

If  for  example,  each  of  two  independent  witnesses,  or  circumstances, 
raises  a  probabiUty  of  6  to  i  in  favour  of  a  certain  event ;  taking  i 
o  ;resrnt  certainly,  i  -  ^  is  the  improbability  of  ^^^  even,  notwith- 
standing each  witness.  Then  |  x  f  ^.V  the  improbabih ty  of  both  prov- 
ing it  Therefore  the  probability  of  the  event  is  48  to  i.  The  matter 
may  be  plainer  if  put  thus  :  A  is  right  6  times  in  7.  or  42  m  49  ;  m  the 
rem'a'nin'g  7  times'in  49  B  will  be  right  6  times.     Therefore,  together 

thev  will  be  right  48  times  in  49.  . 

It  in  an  analogical  argument  there  were  8  points  of  con,panson,  5  fo 
and  \  against  a  certain  inference,  and  the  probabihty  of  each  pent 
::uld'l^'quantified,  the  total  value  of  the  evidence  could  be  esttmated 

'^wZ:ptTo"generaHsations  that  have  not  been  precisely 
quantified  combine  their  evidence,  the  cogency  of  *e  argument  m- 
Tases  in  the  same  way,  though  it  cannot  be  made  -  d^fim^.  H 
he  true  that  most  poets  are  irritable,  and  also  that  most  invalids  are 
frritaJe,  a  stm  greater  proportion  will  be  irritable  of  those  who  are 
both  invalids  and  poets. 

On  the  whole,  from  the  discussion  of  probabilities  there 
emerge  four  principal  cautions  as  to  their  use  :  Not  to  make  a 
pedantic  parade  of  numerical  probability,  where  the  numbers 
have  not  been  ascertained  ;  Not  to  trust  to  our  feelmg  of  what 
is  likely  if  statistics  can  be  obtained  ;  Not  to  apply  an  average 
probability  to  special  classes  or  individuals  without  mqu.rmg 
whether  they  correspond  to  the  average  type  ;  and  Not  to  trust 
to  the  empirical  probability  of  events,  if  their  causes  can  be 
discovered  and  made  the  basis  of  reasoning  which  the  empirical 
probability  may  be  used  to  verify. 

The  reader  who  wishes  to  pursue  this  subject  further  should 
read  a  work  to  which  the  foregoing  chapter  is  greatly  indebted, 
Dr.  Venn's  Logic  of  Chance. 


DIVISION   AND   CLASSIFICATION 


255 


CHAPTER  XXI 
DIVISION  AND  CLASSIFICATION 

§  I.  Classification,  in  its  widest  sense,  is  a  mental  grouping 
of  facts  or  phenomena  according  to  their  resemblances  and 
differences,  so  as  best  to  serve  some  purpose.  I  say  a  "  mental 
grouping  " ;  for  although  in  museums  we  often  see  the  things 
themselves  arranged  in  classes,  yet  such  an  arrangement  only 
contains  specimens  representing  a  classification.  The  classifi- 
cation itself  may  extend  to  innumerable  objects  most  of  which 
have  never  been  seen  at  all.  Extinct  animals,  for  example, 
are  classified  from  what  we  know  of  their  fossils ;  and  some  of 
the  fossils  may  be  seen  arranged  in  a  museum  ;  but  the  animals 
themselves  have  disappeared  for  many  ages. 

Again,  things  are  classed  according  to  their  resemblances 
and  differences  :  that  is  to  say,  those  that  most  closely  resemble 
one  another  are  classed  together  on  that  ground ;  and  those 
that  differ  from  one  another  in  important  ways,  are  distributed 
into  different  classes.  The  more  the  things  differ,  the  wider 
apart  are  their  classes  bo'h  in  thought  and  in  the  arrangements 
of  a  museum.  If  their  differences  are  very  great,  as  with 
animals,  vegetables  and  minerals,  the  classing  of  them  falls  to 
different  departments  of  thought  or  science,  and  is  often  repre- 
sented in  different    museums,  zoological,  botanical,  minera- 

logical. 

We  must  not,  however,  suppose  that  there  is  only  one  way 
of  classifying  things.  The  same  objects  may  be  classed  in 
various  ways  according  to  the  purpose  in  view.  For  gardening, 
we  are  usually  content  to  classify  plants  into  trees,  shrubs, 


flowers,  grass  and  weeds ;  the  ordinary  crops  of  English  agri- 
culture are  distinguished,  in  settling  their  rotation,  into  white 
and  green ;    the  botanist   writes   about   monocotyledons  and 
dicotyledons.     The  principle  of  resemblance  and  difference  is 
recognised    in   all   these   cases ;    but   what   resemblances   or 
differences  are  important  depends  upon  the  purpose  to  be  served. 
Purposes,  however,  may  themselves  be  classified ;  and  here 
the  most  important  distinction  for  our  purpose  (that  is,   in 
Logic)  is  into  (a)  special  or  practical  purposes,  as  in  gardening 
or  hunting,  and  (i3)  general  or  scientific,  as  in  Botany  or  Zoology. 
The  scientific  purpose  is  merely  knowledge,  which  may  indeed 
subserve  all  particular  or  practical  ends,  but  has  no  other  end 
than  knowledge  directly  in  view.     Most  of  what  a  logician  says 
about  classification  is  applicable  to  the  practical  kind ;  but  the 
scientific  (often  called  '  Natural  Classification '),  as  the  most 
thorough  and  comprehensive,  is  what  he  keeps  most  constantly 
before  him. 

Scientific   classification,   of  course,   comes   late    in   human 
history,  and  at  first  works  over  earlier  classifications  which 
have  been  made  by  the  growth  of  intelligence,  of  language,  and 
of  the  practical  arts.     Even  in  the  distinctions  recognised  by 
animals,  may  be  traced  the  grounds  of  classification.     A  cat 
does  not  confound  a  dog  with  one  of  its  own  species,  nor 
water   with   milk,   nor   cabbage   with  fish.     But  it  is  in  the 
development  of  language  that  the  progress  of  instinctive  classi- 
fication may  best  be  seen.     The  use  of  general  names  implies 
the  recognition  of  classes  of  things  corresponding  to  them, 
which  form  their  denotation,  and  whose  resembling  qualities, 
so  far  as  recognised,  form  their  connotation ;  and  such  names 
are  of  many  degrees  of  generality.     The  use  of  abstract  names 
shows  that  the  objects  classed  have  also  been  analysed,  and 
that  their  resembling   qualities  have  been  recognised  amidst 
diverse  groups  of  qualities. 

Of  the  classes  marked  by  popular  language  it  is  worth  while 
to  distinguish  two  sorts  {cf.  chap.  xix.  §  4) ;  Kinds,  and  those 
•having  but  few  points  of  agreement. 


ii 


256      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

But  the  popular  classifications,  made  by  language  and  the 
primitive  arts,  are  very  imperfect.     They  omit  innumerable 
things  which  have  not  been  found  useful  or  noxious,  or  have 
been  inconspicuous,  or  have  not  happened  to  occur  m  the 
region  inhibited  by  those  who  speak  a  particular  language  ; 
and  even  things  recognised  and  named  may  have  been  very 
superficially  examined,  and  therefore  wrongly  classed,  as  when 
a  whale  or  porpoise  is  called  a  fish,  or  a  slowworm  is  con- 
founded with  snakes.     A  scientific  classification,  on  the  other 
hand,  aims  at  the  utmost  comprehensiveness,  ransacking  the 
whole  world  from  the  depths  of  the  earth  to  the  remotest  star 
for  new  objects,  and  scrutinising  everything  with  the  aid  of 
crucible  and  dissecting  knife,  microscope  and  spectroscope,  to 
find  the  qualities  and  constitution  of  everything,  in  order  that 
it  may  be  classed  among  those  things  with  which  it  has  most 
in  common  and  distinguished  from  those  other  things  from 
which  it  differs.     A  scientific  classification  continually  grows 
more  comprehensive,  more  discriminative,  more  definitely  and 
systematically  coherent.     Hence  the  uses  of  classification  may 

be  easily  perceived. 

§  2.  The  first  use  of  classification  is  the  better  understanding 
of  the  facts  of  Nature  (or  of  any  sphere  of  practice)  ;  for  under- 
standing consists  in  perceiving  and  comprehending  the  likeness 
and  difference  of  things,  in  assimilating  and  distinguishing 
them;  and  in  carrying  out  this  process  systematically  new 
correlations  of  properties  are  continually  disclosed.  Thus 
classification  is  closely  analogous  to~we  may  say,  a  kind  of— 
explanation.  Explanation  has  been  shown  (chap.  xix.  §  5)  to 
consist  in  the  discovery  of  the  laws  or  causes  of  changes  in 
Nature;  and  laws  and  causes  imply  similarity,  or  like  changes 
under  like  conditions :  in  the  same  way  classification  consists 
in  the  discovery  of  resemblances  in  the  things  that  undergo 
change.  We  may  say  (subject  to  subsequent  qualifications) 
that  Explanation  analyses  Nature  in  its  dynamic,  Classification 
in  its  static  aspect.  In  both  cases  we  have  a  feeling  of  relief. 
When  the  cause  of  any  event  is  pointed  out,  or  an  object  is 


DIVISION   AND   CLASSIFICATION 


257 


assigned  its  place  in  a  system  of  classes,  the  gaping  wonder, 
or  confusion,  or  perplexity,  occasioned  by  an  unintelligible 
thing,  or  (worse)  by  a  multitude  of  such  things,  is  dissipated. 
No  doubt,  some  people  are  more  than  others  susceptible  of 
this  pleasure  and  fastidious  about  its  purity. 

A  second  use  of  classification  is  to  aid  the  memory.  It 
strengthens  memory,  because  one  of  the  conditions  of  our 
remembering  things  is,  that  they  resemble  what  we  last  thought 
of;  so  that  to  be  accustomed  to  study  and  think  of  things  in 
classes  must  gre.itly  facilitate  remembrance.  But,  besides  this, 
it  improves  the  character  of  memory,  by  making  us  more  likely 
to  remember  what  we  want.  For  what  we  want  in  any  emer- 
gency is  to  remember  what  served  the  purpose  in  similar  cases ; 
or  to  recall  cases  similar  to  the  present  one,  as  in  warding  a 
blow,  or  solving  a  problem,  or  illustrating  an  essay.  Here 
again,  explanation  and  classification  have  the  same  use :  they 
both  tend  to  rationalise  the  memory,  and  to  organise  the  mind 
in  correspondence  with  Nature. 

Every  one  knows  how  a  poor  mind  is  always  repeating  itself,  going  by 
rote  through  the  same  train  of  words,  ideas,  actions ;  and  that  such  a 
mind  is  neither  interesting  nor  practical.  It  is  not  practical,  because 
the  circumstances  of  life  are  rarely  exactly  repeated,  so  that  it  is  rarely 
enough  for  our  present  purpose  to  remember  only  one  former  case ;  we 
need  several,  that  by  comparing  (perhaps  automatically)  their  resem- 
blances and  differences  with  the  one  before  us.  we  may  select  a  course 
of  action,  or  a  principle,  or  a  parallel,  suited  to  our  immediate  needs. 

Thus,  greater  fertility  and  flexibility  of  thought  seem  naturally  to 
result  from  the  practice  of  explanation  and  classification.  But  it  must 
be  honestly  added,  that  the  result  depends  upon  the  spirit  in  which 
such  study  is  carried  on ;  for  if  we  are  too  fond  of  finality,  too  eager  to 
believe  that  we  have  already  attained  a  greater  precision  and  compre- 
hension than  are  in  fact  attainable,  nothing  can  be  more  petrific  than 
•  science,'  and  our  last  state  may  be  worse  than  the  first.  Of  this, 
students  of  Logic  have  often  furnished  examples. 

§  3.  Classification  may  be  either  Deductive  or  Inductive ; 
that  is  to  say,  in  the  formation  of  classes,  as  in  the  proof  of 
propositions,  we  may,  on  the  whole,  proceed  from  the  more  to 
the  less,  or  from  the  less  to  the  more  general :  not  that  these 
two  processes  are  entirely  independent. 

R 


2=8      LOGIC;   DEDUCTIVE   AND   INDUCTIVE 

If  we  begin  with  some  large  class,  such  as  'Animal.'  and  subdivide  it 
deductivei;  into    Vertebrate   and   Invertebrate,    yet   the   P^-pl;^^ 
division  (namely,  central  structure)  has  first  been  -^f;^  ^^^^^ 
parison  of  examples  and  by  generalisation;    if,  on    the   other   hand 
beginning  with  individuals,  we  group  them  inductively  into  "  and 
these  again  into  wider  ones  (as  dogs.  cats,  horses,  whales  and  monkeys 
into  mammalia)  we  are  guided  both  in  special  cases  by  ^P^^^^^ll^ 
the   best   grounds   of    resemblance,   and    throughout   by     he   general 
pr  nciple  of  classification-to  associate  things  that  are  alike  and    o 
separate  things  that  are  unlike.     This  principle  holds  implicit  y  a  place 
in  classification  similar  to  that  of  causation  in  inductive  proof .  and 
whatever  the  remote  origin  or  basis  of  these  principles,  that  is  a  question 
for  Psvchologv  or  for  Metaphysics :  they  are  now  principles  of  inteHi- 
gence.'  of  Logic  and  of  Science.     Here,  therefore,  as  in  proo    induction 
I  implied  in  deduction,  and  deduction  in   inductK>n.     Still,  the  two 
modes  of  procedure  maybe  usefully  distinguished:  \n  deducUon   xve 
advance  from  a  whole  to  its  parts,  from  general  to  special  .m  induction, 
from  special  (or  particular)  to  general,  from  the  parts  to  their  whole. 

§  4.  The  process  of  Deductive  Classification,   or    Formal 
Division,  may  be  represented  thus  : 

A 


AB 


Ab 


ABC 


ABc 


AbC 


I 
Abe 


Given  any  class  (A)  to  be  divided. 

I  Select  one  important  character,  attribute,  or  quality  l^)-  "^^ 
common  to  all  the  individuals  comprehended  in  the  class,  as  the  basis 
of  division  [futidameiitum  divisionis). 

2.  Proceed  by  Dichotomy;  that  is.  cut  the  given  class  ^^^o  two  one 
having  the  selected  attribute  (say.  B).  the  other  not  having  it  (b).  Ihis 
like  all  formal  processes,  assumes  the  principles  of  Contradiction  and 
Excluded  Middle,  that  '  No  A  is  both  B  and  not-B.'  and  that  '  Every  A 
is'eitherBor  not-B'  (chap.  vi.  §  3);  and  if  these  principles  are  not 
true,  or  not  applicable,  the  method  fails. 

When  a  Class  is  thus  subdivided,  it  may  be  called,  in  relation  to  its 
Subclasses,  a  Genus;  and  in  relation  to  it.  the  Subclasses  may  be 
called  Species  :  thus -Genus  A,  Species  AB  and  Ab,  ^^'^■ 

3  Proceed  gradually  in  the  order  of  the  importance  of  characters , 
that  is.  having  divided  the  given  class,  subdivide  on  the  same  principle 
the  two  classes  thence  arising;  and  so  again  and  again,  step  by  step, 
until  all  the  characters  are  exhausted:  Divisio  ne  fiat  per  saltiim. 


DIVISION   AND   CLASSIFICATION 


259 


Suppose  we  were  to  attempt  an  exhaustive  classification  of  things  by 
this  method,  we  must  begin  with  'All  Things.' and  divide  them  (say) 
into  phenomenal  and  not-phenomenal,  and  then  subdivide  phenomena, 
and  so  on,  thus : 

All  Things 


Phenomenal 


Not-phenomenal 


I 


Extended  Unextended 

{e.g.,  Pleasure  and  Pain) 


Resistant 
(Matter) 


Non-resistant 
(Space) 


Gravitating        Non-gravitating 


Simple 


Compound 


Having  subdivided  '  Simple '  by  all  possible  characters,  we  must  then 
go  back  and  similarly  subdivide  Not-phenomenal.  Unextended,  Non- 
resistant,  Non-gravitating  and  Compound.  Now,  if  we  knew  all  possible 
characters,  and  the  order  of  their  importance,  we  might  prepare  a  priori 
a  classification  of  all  possible  things ;  at  least,  of  all  things  that  come 
under  the  principles  of  Contradiction  and  Excluded  Middle.  It  might, 
indeed,  appear  that  many  of  our  compartments  had  nothing  actual 
answering  to  them;  there  may.  for  example,  be  nothing  that  is  not 
phenomenal  to  some  mind,  or  nothing  that  is  extended  and  non-resistant 
(no  vacuum),  and  so  forth.  It  is  true  that  this  implies  a  breach  of  the 
rule,  that  the  dividing  quality  be  not  common  to  the  whole  class;  but. 
in  fact,  doubts  have  been,  and  are.  seriously  entertained  whether  these 
compartments  are  filled  or  not.  If  they  are  not,  we  have  concepts 
representing  nothing,  which  have  perhaps  been  generated  by  the  mere 
force  of  grammatical  negation ;  and,  on  the  strength  of  these  empty 
concepts,  we  have  been  misled  into  dividing  by  an  attribute,  which 
(being  universal)  cannot  be  a  fundamentum  divisionis.  But  though 
places  might  be  empty,  there  would  be  a  place  for  everything;  for 
whatever  did  not  come  into  some  positive  class,  such  as  Gravitating, 
must,  at  any  rate,  fall  under  one  of  the  negative  classes  (the  'Nots'j 
that  would  run  down  the  right-hand  side  of  the  Table  and  of  its  sub- 
divisions. 

This  is  the  ideal  of  classification.     Unfortunately,  however,  we  have 
to  learn  what  characters  or  attributes  are  possible,  by  experience  and 


.6o      LOGIC :    DEDUCTIVE   AND   INDUCTIVE 

comparison;  we  are  far  fro.  Unowing  ^^:i:^'-Z^  ZX^or^' 
the  order  of  their  importance  ;  nor  are  ^ve  even  c  ea    vvh     _       P  ^^  ,  ^^ 

means  in  this  context,  -hef-^ '  ^'-^f^  P^^.^^'H^nce,  in  classifying 
•causally  influential,;  or;  -dKattve  of  oAe^-    .."fth  particular  things, 
actual  things,  the  inducUve  ■-*°f/,  .'^^tT^I^^'discovered  by  investiga- 
and  sorting  them  accordmg  to  «*'«'Y'^^^"^!'/„3„,ed  to.    The  excep- 
tion of  their  nature,  must  nearly  '■^l^J.'^J^^'^tnr  where  certain 
tional  cases,  in  which  deduction  is  -^e^'y  ~  °^^"      ^^  ^e  known, 
limits  to  the  number  and  combination  of  q"^''''-  ^^PP^^  mathematical 
as  they  may  -J;;^-- --^'t:  dS  "^ of  Architecture 
rrre  itiir 'rtr^s^nd  s.an.as  of  Hng,.h  Poe^-— - 
fact,  these  things  are  too  free,  subtle  and  -mplex  fo  ^^^^  ^^^ 

ment :  for  do  not  the  Arts  grow  like  trees  ■  J^J J         ^^ree  kinds 
mathematical;  as  «e  may  ^^ow  that  the  e  a-  poss  y^^ 

of  plane  triangles,  four  conic  sections,  hve  re„uia 

§  5    The  rules  for  /esfing  a  Division  are  as  follows  : 

,  Each  Sub-class,  or  Species,  should  comprise  less  than  the  Class, 

or  Genus,  to  be  divided.  v   n  u^  ^  rpal  one   and  not  based 

This  provides  that  the  ^^^^^^^^^  ^J ^l^Leiore.  .^e  f^rst 

upon  an  attribute  ---°" '°  .'^^^^^.^ten Completely  adhered  to.     But, 
rule  for  making  a  division  shall  ha  e  ^ee"  co    p        y  ^^ 

as  in  §  4.  we  are  here  met  by  a  ogical  f ";  J^"PP°;,,  g,  into  AB 
be  divided  is  A,  and  we  attempt .'«  ^'vide  upon  the  a«  ^  ^^^^  .^ 

and  Ab:  is  this  now  a  'rue  division    if  -e  do  not  y^  ^  ^^  ^^^ 

not  B  ?    As  far  as  our  knowledge  extends,  w    hav    n^^  .^  ^^^^^ 

But.  on  the  other  hand,  our  knowledge  o 
exhaustive;  so  that, althcnigh we  know o^n    A  *^^^ 
exist,  and  we  have  seen  that       is  a  >o    <=  ^^.^     ^^  ,,,,,  ,,  .^ems  better 
we  do  not  know.     In  a  aeauciue  c  division      Hence,  in 

to  regard  every  attribute  as  y^os^Uejro.n^of^^^^^^      ^^^^^^^^_ 

the  above  d---  °  ^^J^^^f^J^^..^^  ,  ,p%ar  as  negative  classes 
Non-resistant,  Resistant  in uu  g^  r  ^„  ^ttrihute^  although  their  real 
(that  is,  classesbased  on  the  nega- of    n  attnbute)^^^^  ^^^  g^^^^  ^^^^^^ 

existence  may  be  doubtful     ^ut,  i    tnis       j  ^  ^^^^-^i 

---'^^^-^thl  dtrrb^dlvide^/'     ^else  we  must  confine 
comprise  less  than  the  class  to  ;    dividing  Colour  into 

the  rule  to  (a)  thoroughly  empirical  divisions,  as'  »     ^^^     ^^^ 

Red  and  Not-red,  where  we  know  that  both  sub  ^^  ^^^^^ 

(6)  divisions  under  demonstrable  -"^u^^^^-^  ;t-now  that  it  is  only 

Tr^tb^ctr SkfntX  should  be  e.ual  to  the  Class  to  be 


DIVISION    AND   CLASSIFICATION 


261 


divided  :  the  sum  of  the  Species  constitutes  the  Genus.  This  provides 
that  the  Division  shall  be  exhaustive;  which  is  always  secured  by- 
dichotomy,  according  to  the  principle  of  Excluded  Middle  ;  because 
whatever  is  not  in  the  positive  class,  must  be  in  the  negative  :  Red  and 
Not-red  include  all  colours. 

3.  The  Sub-classes  must  be  opposed  or  mutually  exclusive :  Species 
must  not  overlap.  This  again  is  secured  by  Dichotomy,  according  to 
the  principle  of  Contradiction,  provided  the  Division  be  made  upon  one 
attribute  at  a  time.  But,  if  we  attempt  to  divide  simultaneously  upon 
two  attributes,  as  '  Musicians  '  upon  '  nationality  '  and  '  method,'  we  get 
what  is  called  a  Cross-division,  thus:  'German  Musicians,'  'Not- 
German,'  '  Classical,'  '  Not-Classical,'  for  these  classes  may  overlap,  the 
same  men  sometimes  appearing  in  two  groups — Bach  in  '  German '  and 
'  Classical,' Pergolesi  in  'Not-German'  and  'Classical.'  If,  however, 
we  divide  Musicians  upon  these  attributes  successively,  cross  division 
will  be  avoided,  thus  : 

Musicians 


Classical 


Non-classical 


German        Non-German 


German        Non-German 


Here  no  Musician  will  be  found  in  two  classes,  unless  he  has  written 
works  in  two  styles,  or  unless  there  are  works  whose  style  is  undecided. 
Let  this  "  unless— or  unless  "  suggest  caution  in  using  dichotomy  as  a 
short  cut  to  the  classification  of  realities. 

4.  No  Sub-class  must  include  anything  that  is  not  comprised  in  the 
class  to  be  divided  :  the  Genus  comprises  all  the  Species.  Do  not 
divide  Dogs  into  fox-terriers  and  dog-fish. 

§  6.  The  process  of  Inductive  Classification  may  be  repre- 
sented thus : 

Given  any  multitude  of  individuals  to  be  classified  : 
(i)  Place  together  in  groups  (or  in  thought)  those  things  that 
have  in  common  the  most,  the  most  widely  diffused  and  the 
most  important  qualities. 

(2)  Connect  those  groups  which  have,  as  groups,  the  greater 
resemblance,    and    separate    those     that    have    the    greater 

difference. 

(3)  Demarcate,  as  forming  higher  or  more  general  classes, 
those  groups  of  groups   that   have   important   characters   in 


262      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

common ;  and,  if  possible,  on  the  same  principle,  form  those 
higher  classes  into  classes  higher  still :  that  is  to  say,  graduate 
the  classification  upwards. 

Whilst,  in  Division,  the  terms  'Genus'  and  'Species'  are  entirely 
relative  to  one  another  and  have  no  fixed  positions  in  a  gradation  of 
classes,  it  has  been  usual,  in  Inductive  Classification,  to  confine  the 
term  '  Species '  to  classes  regarded  as  lowest  in  the  scale,  to  give  the 
term  '  Genera'  to  classes  on  the  step  above,  and  at  each  higher  step  to 
find  some  new  term,  such  as  'Tribe,'  'Order,'  'Sub-kingdom,' 
'Kingdom';  as  may  be  seen  by  turning  to  any  book  on  Botany  or 
Zoology.  If.  having  fixed  our  Species,  we  find  them  subdivisible,  it  is 
usual  to  call  the  Sub-species  '  Varieties.' 

Suppose  we  attempt  to  classify  by  this   method  the  objects  m   an 
ordinary  sitting-room.      We  see  at  a  glance  carpets,   mats,  curtains, 
grates,  fire-irons,  coal-scuttles,   chairs,   sofas,   tables,   books,    pictures, 
musical  instruments,  etc.     These  we  may  call  '  Species.'     Carpets  and 
mats  clearly  go  together  ;  so  do  chairs  and  sofas ;  so  do  grates,  fire- 
irons,  and  coalscuttles ;  and  so  on.     These  greater  groups,  or  higher 
classes,  we  may  call  'Genera.'     Putting  together  carpets,  mats  and 
curtains  as  'warmth-fabrics';  chairs,  sofas  and  tables  as  'supports'; 
books,  pictures  and  musical  instruments  as  '  means  of  culture ' :  these 
groups  we  mav  call  Orders.     Sum  up  the  whole  as,  from  the  house- 
wife's point  of  view,  'furniture.'     If  we  then  subdivide  some  of  the 
species,  as  books   into  poetry,  novels,   travels,  etc.,  these  Sub-species 
may  be  considered  '  varieties.' 

A  Classification  thus  made,  may  be  tested  by  the  same  rules  as  those 
given  for  testing  a  Division ;  but  if  it  does  not  stand  the  test,  we  must 
not  infer  that  the  classification  is  a  bad  one.  If  the  best  possible,  it  is 
good  though  formally  imperfect :  whatever  faults  are  found  must  then 
be  charged  upon  the  'matter,'  which  is  traditionally  perverse  and 
intractable.  If.  for  example,  there  is  a  hammock  in  the  room,  it  must 
be  classed  not  with  the  curtains  as  a  warmth- fabric,  but  with  the  sofas 
as  a  support  •  and  books  and  pictures  may  be  classed  as.  in  a  peculiar 
sense  means  of  culture,  though  all  the  objects  in  the  room  may  have 
been  modified  and  assorted  with  a  view  to  gratifying  and  developing 
good  taste. 

§  7.  The  difficulty  of  classifying  natural  objects  is  very 
great.  It  is  not  enough  to  consider  their  external  appearance  : 
exhaustive  knowledge  of  their  internal  structure  is  necessary, 
and  of  the  functions  of  every  part  of  their  structure.  This  is 
a  matter  of  immense  research,  and  has  occupied  many  of  the 


DIVISION   AND   CLASSIFICATION 


263 


greatest  minds  for  very  many  years.     The  following  is  a  tabular 
outline  of  the  classification  of  the 

Animal  Kingdom 


Sub-kingdom:     Vertebrates 


Invertebrates  (5  Sub-kingdoms) 


Sauropsida 


Ichthyopsida 


Class: 


Mammals       Birds     Reptiles     Amphibia     Fishes 


Sub-class  :        Placental 


Division  :        Monodelphia 


Implacental 


Didelphia 


Ornithodelphia 


I  I  I  I  I 

O'^DER :  Quadrumana     Rodentia    Carnivora    Ungulata    Caetacea,  etc. 


Section 


Pinnigrada        Plantigrada        Digitigrada 

I  I 

( Seals,  etc. )         ( Bears,  etc. ) 


Genus:         Mustelidae        Viverridae     Hya^nidae     Canidae     Felidae 

(Weasels,  etc.)     (Civets,  etc.) 


Lion       Tiger       Leopard      Puma       Lynx       Cat,  etc. 


Species  : 


Variety  :  African        Syrian        Cave-lion  (extinct) 

As  there  is  not  space  enough  to  tabulate  such  a  classification 
in  full,  I  have  developed  at  each  step  the  most  interesting 
groups :  Vertebrates,  Mammals,  Monodelphia,  Carnivora,  Digi- 
tigrada, Felidse,  Lion.  Most  of  the  other  groups  in  each  grade 
are  also  subdivisible,  though  some  of  them  contain  far  fewer 
sub-classes  than  others. 

To  see,  however,  the  true  character  of  this  classification,  we 
must  consider  that  it  is   based   chiefly  upon   knowledge   of 


264      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

existing  animals.  Some  extinct  animals,  known  by  then: 
fossilsffind  places  in  it;  for  others  new  places  have  been 
made.  But  it  represents,  on  the  whole,  a  cross  section,  or 
cross-sections,  of  Nature  as  developing  in  time ;  and,  in  order 
Tg  ve  a  just  view  of  the  relations  of  animals,  it  must  be  seen 
in  the  light  of  other  considerations.      The  older  systems  of 

this  system  are  determined  by  quantity  of  resemblance  in 
co-existent  qualities,  as  the  ground  of  their  afhnity. 

§  8.  Darwin's  doctrine  of  the  origin  of  species  modifies    he 
conception  of  natural  classification  in  several  ^^ays^    In  the 
first  pLe,  if  all  living  things  are  blood-relations    modifi^^^^^ 
the  course  of  ages  according  to  their  various  conditions  of  life 
'Affinity'  must  mean  '  nearness  of  common  descent  ;  and  it 
seems  irrational  to  propose  a  classification  upon  any  other 
basis      We  have  to  consider  the  Animal  (or  the  Vegetable) 
Kingdom  as  a  family  tree,  exhibiting  a  long  fine  of  ancestors, 
and  (descended  from  them)  all  sorts  of  cousins,  first,  second 
third    ./..,   perhaps   once,  twice,    or   oftener   '  removed       Of 
course,  animals  in  the  relation  of  first  cousins  must  be  classed 
as  nearer  than  second  cousins,  and  so  on. 

But,  if  we  accept  this  principle,  and  are  able  to  trace 
relationship,  it  may  not  lead  to  the  same  results  as  we  should 
reach  by  simply  relying  upon  the  present  quantity  of 
resemblance ',  unless  we  understand  this  in  a  very  particular 
way  For  the  most  obvious  features  of  an  animal  may  have 
been  recently  acquired,  as  often  happens  with  those  characters 
which  adapt  an  animal  to  its  habits  of  life,  as  the  wings  of  a 
bat  or  the  fish-like  shape  of  a  dolphin ;  or  as  in  cases  of 
'mimicry'.  Some  butterflies,  snakes,  efc,  have  grown  to 
resemble  closely,  in  a  superficial  way,  other  butterflies  and 
nakes  from  which  a  stricter  investigation  widely  separates 
them -'and  this  superficial  resemblance  is  probably  a  recent 
acquisition,  for  the  sake  of  protection  :  the  imitated  butterflies 


DIVISION    AND   CLASSIFICATION 


265 


being  nauseous,  and  the  imitated  snakes  poisonous.  On  the 
other  hand,  ancient  and  important  traits  of  structure  may,  in 
some  species,  have  dwindled  into  inconspicuous  survivals,  or 
be  still  found  only  in  the  embryo ;  so  that  only  great  know- 
ledge and  sagacity  can  identify  them  ;  yet  upon  ancient  traits, 
though  hidden,  classification  depends.  The  seal  seems  nearer 
allied  to  the  porpoise  than  to  the  tiger,  the  shrew  nearer  to 
the  mouse  than  to  the  hedgehog ;  and  the  Tasmanian  hyaena, 
or  the  Tasmanian  devil,  looks  more  like  a  true  hyaena,  or  a 
badger,  than  like  a  kangaroo ;  yet  the  seal  is  nearer  akin  to 
the  tiger,  the  shrew  to  the  hedgehog,  and  the  Tasmanian 
carnivores  are  marsupial,  like  the  kangaroo.  To  overcome 
this  difficulty  we  must  understand  the  resemblance  upon 
which  classification  is  based  to  include  resemblance  of 
Causation,  that  is,  the  fact  itself  of  descent  from  common 
ancestors.  In  the  case  of  organic  beings,  all  other  rules  of 
classification  are  subordinate  to  one :  trace  the  genealogy  of 
every  form. 

By  this  rule,  however,  we  get  a  definite  meaning  for  the 
phrase  'important  or  fundamental  attribute'  as  determining 
organic  classes ;  namely,  most  ancient,  or  '  best  serving  to 
indicate  community  of  origin'.  Grades  of  classification  will 
be  determined  by  such  fundamental  characters,  and  may  cor- 
respond approximately  to  the  more  general  types  (now  mostly 
extinct)  from  which  existing  animals  have  descended. 

In  the  second  place,  by  the  hypothesis  of  development  the 
fixity  of  species  is  discredited.  The  lowest  grade  of  a 
classification  is  made  up  not  of  well-defined  types  un- 
changing from  age  to  age,  but  of  temporary  species,  often 
connected  by  uncertain  and  indistinct  varieties :  some  of 
which  may,  in  turn,  if  the  conditions  of  their  existence 
alter,  undergo  such  changes  as  to  produce  new  species. 
Hence,  again,  the  notion  that  Kinds  exist  in  organic  nature 
must  be  greatly  modified.  During  a  given  period  of  a 
few  thousand  years,  Kinds  may  be  recognised;  because, 
under   such    conditions  as  now  prevail   in   the   world,    that 


i 


266      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 
period  of  time  is  insufficient  to  bring  about  g-^ft  changes. 
But,  if  it  be  true  that  lions,  tigers,  and  leopards  have  had 
a   common   ancestor,   from  whose  type  ihey  have  gradual  y 
diverged,  it  is  plain  that  their  present  distinctness  results  only 
from  the  death  of  intermediate  specimens  and  the  destruction 
of  intermediate   varieties.      Could   we,    by   the   evidence   o 
fossils,  restore  all  the   ranks   of  the   great   processions   that 
have  descended  from  the  common  ancestor,  we  should  find 
nowhere   a    greater   difference    than    between    offspring   and 
parents ;   and  the  appearance   of   Kinds   existing  in  nature 
which  is  so  striking  in  a  museum  or  zoological  garden,  would 
entirely  vanish. 

A  classification,  then,  as  formerly  observed,  represents  -  "---'^^ 
of  nature  as  developing  in  time :  could  we  begm  at  the  beg—  and 
follow  this  development  down  the  course  of  time,  we  should  find  no 

clisses,  but  an  ever  moving,  changing,  ^P-^^^f ' ''-"^'^'"^'^t " » 
It  mav  be  represented  thus ;  Suppose  an  animal  (or  plant)  A,  extendmg 
over  ascertain  geographical  area,  subject  to  different  influences  and  con- 
d  ttons  of  climlterfood,  hill  and  plain,  wood  and  prairie,  enemies  and 
rivals,  and  undergoing  modifications  here  and  there  in  ^^ap  ation  to  he 
varying  conditions  of  hfe :  then  varieties  appear.  These  varieties 
diverging  more  and  more,  become  distinct  Species  (AB,  AC,  AD,  AX). 

Some  of  these  Species,  the  more  widely  '^>ff"^^<'' ^S^\"  P^^f  ""S  ™m\tse' 
which,  in  turn,  become  Species  (ABE,  ABF,  ADG^ADH).     From  these, 
again,  arise  ABFI,  ABFJ ,  ADHK,  ADHL,  ADHM.     Then  ABE   ABF 
and  ADH   are   Genera  (ADG   being  extinct) ;   and  the  earlier  types 
represent  Families  and  Orders. 


DIVISION   AND   CLASSIFICATION 


267 


ABL 


ABFI 


ADHK    ADHL    ADHM 


If  in  this  age  a  classifier  appears,  he  finds  seven  living  Species  which 
can  be  grouped  into  four  Genera  (ABE.  ABF.  AC.  ADH).  and  these 


again  into  three  Families  (AB,  AC,  AD),  all  forming  one  Order.  If  the 
fossils  of  ADG  and  AX  can  be  found,  he  has  two  more  Species,  one 
more  Genus  (ADG).  and  one  more  Family  (AX).  For  AC,  which  has 
persisted  unchanged,  and  AX,  which  has  become  extinct,  are  both  of 
them  Families,  each  represented  by  only  one  Species. 

But  now  suppose  that  he  could  find  a  fossil  specimen  of  every 
generation  (hundreds  of  thousands  of  generations),  from  ABFI.  etc.,  up 
to  A ;  then,  as  each  generation  would  only  differ  from  the  preceding  as 
offspring  from  parents,  he  would  be  unable  at  any  point  to  distinguish  a 
Species ;  at  most,  he  would  observe  a  slightly  marked  variety.  ABFI 
and  ABFJ  would  grow  more  and  more  alike,  until  they  became  indis- 
tinguishable in  ABF ;  ABF  and  ABE  would  merge  into  AB ;  AB,  AC, 
AD  and  AX  would  merge  into  A.  Hence,  the  appearance  of  Species  is 
due  to  our  taking  cross-sections  of  time,  or  comparing  forms  that  belong 
to  periods  remote  from  one  another  (like  AX.  ADG.  and  ADHK.  or  AD. 
ADH  and  ADHK),  and  this  appearance  of  Species  depends  upon  the 
destruction  of  ancestral  intermediate  forms. 

In  the  third  place,  the  hypothesis  of  development  modifies 
the  logical  character  of  classification  :  it  no  longer  consists  in 
a  direct  induction  of  co-existent  characters,  but  is  largely  a 
deduction  of  these  from  the  characters  of  earlier  forms, 
together  with  the  conditions  of  variation;  in  other  words, 
the  definition  of  a  species  must,  with  the  progress  of  science, 
cease  to  be  a  mere  empirical  law  of  co-existence  and  become 
a  derivative  law  of  Causation.  But,  after  all,  this  was  already 
implied  in  the  position  that  causation  is  the  fundamental 
principle  of  the  explanation  of  concrete  things ;  and,  accord- 
ingly, the  derivative  character  of  species  or  kinds  extends 
beyond  organic  nature. 

§  9.  The  classification  of  inorganic  bodies  also  depends  on 
causation.  There  is  the  physical  classification  into  Solids, 
Liquids,  and  Gases.  But  these  states  of  matter  are  dependent 
on  temperature ;  at  least,  it  is  known  that  many  bodies  may, 
at  different  temperatures,  exist  in  all  three  states.  They 
cannot  therefore  be  defined  as  solid,  liquid,  or  gaseous 
absolutely,  but  only  within  certain  degrees  of  temperature, 
and  therefore  as  dependent  upon  causation.  Similarly,  the 
geological  classification  of  bodies,  according  to  relative  anti- 
quity (primary,   secondary,  tertiary,  with  their  subdivisions), 


268      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

and  mode  of  formation  (igneous  and  aqueous),  rests  upon 
causation;  and  so  does  the  chemical  classification  of 
compound  bodies  according  to  the  elements  that  enter  into 
them  in  definite  proportions.  Hence,  only  the  classification 
of  the  elements  themselves  (amongst  concrete  things),  at 
present,  depends  largely  upon  empirical  Co-existence.  If  the 
elements  remain  irresolvable  into  anything  simpler,  the  defini- 
tions of  the  co-existent  characters  that  distinguish  them  must 
be  reckoned  amongst  the  ultimate  Uniformities  of  Nature. 
But  if  a  definite  theory  of  their  origin  both  generally  and  seve- 
rally, whether  out  of  ether  vortices  or  what-not,  shall  ever  gain 
acceptance,  similarity  of  genesis  or  causation  will  naturally  be 
the  leading  consideration  in  classifying  the  chemical  elements. 
In  fact,  the  ultimate  explanation  of  nature  is  always  causation ; 
or,  in  other  words,  the  Law  of  Causation  is  the  backbone  of 
the  system  of  Experience. 


CHAPTER  XXII 


NOMENCLATURE,  DEFINITION,  PREDICABLES 


§  I.  Precision  of  thought  needs  precision  of  language,  not 
only  for  recording  such  thought  and  for  communicating  it  to 
others,  the  two  uses  most  frequently  insisted  upon,  but  even 
for  forming  general  or  abstract  ideas.  It  is  true  that  we  can 
often  remember  with  great  vividness  persons,  things,  landscapes, 
changes  and  actions  of  persons  or  things,  without  the  aid  of 
language  (though  words  are  often  mixed  with  such  trains  of 
imagery),  and  thus  may  form  judgment  and  inferences  in  par- 
ticular cases  ;  but  for  general  notions,  judgments  and  inferences 
not  merely  about  this  or  that  man,  Bismarck  or  Garibaldi,  but 
about  all  men  or  all  Germans,  we  need  something  besides  the 
few  images  we  can  form  of  them  from  observation  or  from 
pictures.  Even  in  those  cases  where  we  may  possess  generic 
images,  say,  of  '  horse '  or  '  cat '  (that  is,  images  formed,  like 
composite  photographs,  by  a  coalescence  of  the  images  of  all 
the  horses  or  cats  we  have  seen,  so  that  their  common  properties 
stand  out  and  their  differences  frustrate  and  cancel  one  another), 
these  are  useless  for  precise  thought ;  for  the  generic  image  will 
not  correspond  with  the  general  appearance  of  horse  or  cat, 
unless  we  have  had  proportional  experience  of  all  varieties  and 
have  been  impartially  interested  in  all ;  and,  besides,  what  we 
want  for  general  thought  is  not  a  generic  image  of  the  appear- 
ance of  things,  though  it  were  much  more  definite  and  fairly 
representative  than  such  images  ever  are,  but  a  general  repre- 
sentation of  their  important  characters ;  which  may  be  con- 
nected with  internal  organs,  such  as  none  but  an  anatomist 


270      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

ever  sees.  We  require  a  symbol  connected  with  the  general 
character  of  a  thing,  or  quality,  or  process,  as  scientifically 
determined,  whose  representative  truth  may  be  trusted  in 
ordinary  cases,  or  may  be  verified  whenever  doubt  arises. 
Such  symbols  are  for  most  purposes  provided  by  language  ; 
Mathematics  and  Chemistry  have  their  own  symbols. 

§  2.  First,  then,  there  should  be  "  a  name  for  every  important 
meaning  "  :  (a)  A  Nomenclature,  or  system  of  the  names  of  all 
classes  of  objects,  adapted  to  the  use  of  each  science.  Thus, 
in  Geology  there  are  names  for  classes  of  rocks  and  strata,  in 
Chemistry  for  the  elements  and  their  compounds,  in  Zoology 
and  Botany  for  the  varieties  and  species  of  animals  and  plants, 
their  genera,  families  and  orders. 

To  have  such  names,  however,  is  not  the  whole  aim  in  forming  a 
scientific  language,  it  is  desirable  that  they  should  be  systematically 
significant,  and  even  elegant.  Names,  like  other  instruments,  ought  to 
be  efficient,  and  the  efficiency  of  names  consists  in  conveying  the  most 
meaning  with  the  least  effort.  In  Botany  and  Zoology  this  result  is 
obtained  by  giving  to  each  species  a  composite  name  which  includes 
that  of  the  genus  to  which  it  belongs.  Thus  the  species  of  Felidae  given 
in  chap.  xvii.  §  7,  are  called  Felis  ho  (lion),  Felis  tigris  (tiger),  Felis 
leopardus  (leopard),  Felis  concolor  (puma),  Felis  lyncus  (European  lynx), 
Felis  catus  (wild  cat).  To  take  another  illustration  from  the  nomen- 
clature of  Butterflies:  Vanessa  Atalanta  (red  admiral),  Vanessa  lo  (pea- 
cock), Vanessa  polycloros  (large  tortoise-shell),  Vanessa  urtica  (small 
tortoise-shell),  Va?iessa  Antiopa  (Camberwell  beauty),  etc.  In  Chemistry, 
again,  the  nomenclature  is  extremely  efficient.  Names  of  the  simpler 
compounds  are  formed  by  combining  the  names  of  the  elements  that 
enter  into  them  ;  as  Hydrogen  Chloride,  Hydrogen  Sulphide,  Carbon 
Dioxide ;  and  these  can  be  given  still  more  briefly  and  efficiently  in 
symbols,  as  HCl,  HjS,  CO,.  The  symbolic  letters  are  usually  initials  of 
the  names  of  the  elements:  as  C  =  Carbon,  S  =  Sulphur;  sometimes  of 
the  Latin  name,  when  the  common  name  is  English,  as  Fe  — -  Iron. 
Each  letter  represents  a  fixed  quantity  of  the  element  for  which  it 
stands,  viz.,  the  atomic  weight.  The  number  written  below  a  symbol 
on  the  right-hand  side  shows  how  many  atoms  of  the  element  denoted 
enter  into  a  molecule  of  the  compound. 

(b)  A  Terminology  is  next  required,  in  order  to  describe 
and  define  the  things  that  constitute  the  classes  designated  by 
the  nomenclature,  and  to  describe  and  explain  their  actions. 


NOMENCLATURE 


271 


(i)  A  name  for  every  integral  part  of  an  object,  as  head,  limb, 
vertebra,  heart,  nerve,  tendon ;  stalk,  leaf,  corolla,  stamen, 
pistil ;  plinth,  frieze,  etc.  (ii)  A  name  for  every  metaphysical 
part  of  an  object  (that  is,  for  every  abstract  quality  of  it,  or  for 
a  quality  considered  apart  from  the  rest  that  constitute  it),  and 
for  their  degrees  and  modes :  as  extension,  figure,  solidity, 
weight ;  rough,  smooth,  elastic,  friable  ;  the  various  colours^ 
red,  blue,  yellow,  in  all  their  shades  and  combinations  ;  and  so 
with  sounds,  smells,  tastes,  temperatures. 

The  terms  of  Geometry  are  employed  to  describe  the  modes  of  figure, 
as  angular,  curved,  square,  elliptical ;  and  the  terms  of  Arithmetic  to 
express  the  degrees  of  weight,  elasticity,  temperature,  pitch  of  sound. 
When  other  means  fail,  qualities  are  suggested  by  the  names  of  things 
which  exhibit  them  in  a  salient  way :  figures  by  such  terms  as 
amphitheatre,  bowl-like,  pear-shaped,  egg-shaped ;  colours  by  lias- 
blue,  sky-blue,  gentian-blue,  peacock-blue ;  and  similarly  sounds,  smells 
and  tastes.  It  is  also  important  to  express  by  short  terms  complex 
qualities,  as  harmony,  fragrance,  organisation,  sex,  symmetry,  stratifi- 
cation. 

(iii)  In  the  explanation  of  Nature  we  require  further  suitable 
names  for  processes  and  activities :  as  deduction,  conver- 
sion, verification,  addition,  integration,  causation,  tendency, 
momentum,  gravitation,  aberration,  refraction,  conduction, 
affinity,  combination,  germination,  respiration,  attention,  asso- 
ciation, development. 

There  may  be  sometimes  a  difficulty  in  distinguishing  the  terms 
which  stand  for  qualities  from  those  that  express  activities,  since  all 
qualities  imply  activities.  Weight,  for  example,  implies  gravitation  ; 
and  the  quality  heat  is  also  a  kind  of  motion.  But  the  distinction 
aimed  at  lies  between  a  quality  as  perceived  by  means  of  an  effect  upon 
our  senses  (as  weight  is  resistance  to  our  effort  in  lifting  ;  heat,  a  sensa- 
tion when  we  approach  fire),  and  that  property  of  a  body  which  is  con- 
ceived to  account  for  its  energy  (as  gravitation  that  brings  a  body  to 
the  ground,  or  physical  heat  that  expands  an  iron  bar  or  works  an 
engine).  The  former  class  of  words,  expressing  qualities,  are  chiefly 
used  in  description  ;  the  latter  class,  expressing  activities,  are  chiefly 
needed  in  explanation.  They  correspond  respectively,  like  classifica- 
tion and  explanation,  with  the  static  and  dynamic  aspects  of  Nature. 

The  terms  of  ordinary  language  fall  into  the  same  classes  as 


272      LOGIC:   DEDUCTIVE   AND    INDUCTIVE 

those  of  science  :  they  stand  for  things,  classes  of  things,  parts, 
or  quahties,  or  activities  of  things  ;  but  they  are  far  less  precise 
in  their  signification.     As  long  as  popular  thought  is  vague  its 
language  must  be  vague  ;  nor  is  it  desirable  too  strictly  to  correct 
the  language  whilst  the  thought  is  incorrigible.     Much  of  the 
effect  of  poetry  and  eloquence  depends  upon  the  elasticity  and 
indirect  suggestiveness  of  common  terms.     Even  in  reasonmg 
upon  some  subjects,  it  is  a  mistake  to  aim  at  an  unattainable 
precision.     It  is  better  to  be  vaguely  right  than  exactly  wrong. 
In  the  criticism  of  manners,  of  fine  art,  or  of  literature,  in 
politics,  religion  and  moral  philosophy,  what  we  are  anxious  to 
say  is  often  far  from  clear  to  ourselves  ;  and  it  is  better  to  indi- 
cate our  meaning  approximately,  or  as  we  feel  about  it,  than  to 
convey  a  false  meaning,  or  to  lose  the  warmth  and  colour  that 
are  the  life  of  such  reflections.     It  is  hard  to  decide  whether 
most  harm  has  been  done  by  sophists  who  take  a  base  advan- 
tage of  the  vagueness  of  common  terms,  or  by  honest  paralo- 
gists  (if  I  may  use  the  word)  who  begin  by  deceiving  themselves 
with  a  plausible  definiteness  of  expression,  and  go  on  to  pro- 
pagate their  delusions  amongst  followers  eager  for  systematic 
insight  but  ignorant  of  the  limits  of  its  possibility. 

§^3.  A  Definition  is  necessary  for  every  scientific  name  (it 
possible).  To  define  a  name  is  to  give  a  precise  statement  of 
its  meaning  or  connotation.  The  name  to  be  defined  is  the 
subject  of  a  proposition,  whose  predicate  is  a  list  of  the  funda- 
mental qualities  common  to  the  things  or  processes  which  the 
subject  denotes,  and  on  account  of  possessing  which  qualities 
this  name  is  given  to  them. 

Thus  acurveis  a  lineofvvhich  no  partis  straight.  The  momentum  of  a 
moving' body  is  the  product  of  its  mass  and  its  velocity  (these  bemg  ex- 
pressed in  numbers  of  certain  units).  Nitrogen  is  a  transparent  colour- 
less gas.  of  specific  gravity  -9713.  "Ot  readily  combining,  etc  A  Lion 
may  be  defined  as  a  monodelphian  mammal,  predatory,  walkmg  on  its 
toes,  of  nocturnal  habits,  with  a  short  rounded  head  and  muzzle  ; 
dental   formula:    Incisors  1^ .  Canines   I_J  .  premolars  1^  , 

molars  '       '  =  30 ;  four  toes  on  the  hind  and  five  on  the  fore  foot, 
1  -  I 


NOMENCLATURE 


273 
retractile  claws,  prickly  tongue,  light  and   muscular  in  build    about 

w  th  a  tufted  tail.  If  anything  answers  to  this  description,  it  is  called 
a  hon  ;  if  not,  not :  for  this  is  the  meaning  of  the  name 

Definition'''?h?t  ^"Tr  l'  ""f^  '"'^'^^  '°  ^'^^  '^^  Incomplete 
Deiinition,    that  IS,  a  list  of  qualities  not  exhaustive,  but  containing 

enough  to  Identify  the  things  denoted  by  the  given  name;  as  Tf  we 
^y  that  a  hon  is  •  a  large  tawny  beast  of  prey  with  a  tufted  ta  • 
Such  purposes  may  also  be  served  by  a  Description;  which  is  tech- 
nically, a  proposition  mentioning  properties  sufficient  to  distinguish  the 

tutZf-       ';°,'  '^f  P-P-'-  'hat  enter  into  the  definition 
as    If  a    hon  is   called    -the    monarch  of   the    desert    that    figures 
in^the  royal  standard,'  or   .that  helps  the  unicorn   to  suppon   the 

§  4-  The  rules  for  testing  a  Definition  are :   I.— As  to  its 
Contents — 

(i)  It  must  state  the  whole  connotation  of  the  name  to  be 

denned. 

(2)  It  must  not  include  any  quality  derivative  from  the  con- 
notation. 

A  breach  of  this  rule  can  do,  indeed,  no  positive  harm,  but  it  is  a 
depar  ure  from  scientific  economy.  There  is  no  need  to  state  in  the 
definition  what  can  be  derived  from  it;  and  whatever  can  be  derived 
that  mrniTer'  "'       '"^*^"'^"'^'i'  demonstration,  should  be  exhibited  in 

Such  a  quality  is  called  a  Proprium. 

(3)  It  must  not  mention  any  circumstance  that  is  not  a  part 
of  the  connotation,  even  though  it  be  universally  found  in  the 
thmgs  denoted.  Such  a  circumstance,  if  not  derivable  from 
the  connotation,  is  called  an  Accident. 

That,  for  example,  the  Lion  at  present  only  inhabits  the  Old  World 
IS  (I  presume)  an  accident ;  if  a  species  otherwise  like  a  Lion  were  found 
m  B  azil.  It  would  not  be  refused  the  name  of  Lion  on  the  score  of  locality 
Whilst  however,  the  rules  of  Logic  have  forbidden  the  inclusion 
of  Proprmm  or  Accident  in  a  Definition,   in  fact  the  definitions  of 

fnr/H^  b"v^       r   ""™"°"   ^""^  attributes   when  characteristic 
Indeed,  definitions  of  superordinate  classes-Families  and  Orders-not 
infrequently  give  qualities  as  generally  found  in  the  subordinateclasses 
and  at  the  same  time  mention  exceptional  cases  in  which  they  do  not 
occur.  ■'         '"' 


274      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

II.__As  to  its  Expression— 

(4)  A  Definition  must  not  include  the  very  term  to  be 
defined,  nor  any  cognate.  In  defining  Lion  we  must  not  repeat 
Mion,'  nor  use  Meonine' ;  it  would  elucidate  nothing. 

(5)  It  must  not  be  put  in  vague  language. 

(6)  It  must  not  be  in  a  negative  form,  if  a  positive  form  is 
obtainable.  We  must  not  be  content  to  say  that  a  lion  is  *  no 
vegetarian,'  or  '  no  lover  of  daylight.'  To  define  a  curve  as  a 
line  *  always  changing  its  direction  '  may  be  better  than  as  '  m 

no  part  straight.' 

§  5.  The  process  of  determining  a  Definition  is  inseparable 
from  classification.     We  saw  that  classification  consists  in  dis- 
tributing things  into  groups  according  to  their  likenesses  and 
differences,  regarding  as  a  class  those  individuals  which  have 
most  qualities  in  common.     In  doing  so  we  must,  of  course, 
recognise  the  common  qualities  or  points  of  likeness  ;  and  to 
enumerate  these  is  to  define  the  name  of  the  class.      If  we 
discover  the  qualities  upon  which  a  class  is  based  by  direct 
observation  and  induction,  by  the  same  method  we  discover 
the  definition  of  its  name  ;   and  similarly  if  we  discover  the 
qualities  of  the  class  by  the  help  of  both   observation   and 
deduction,   as    in    the    modern   classification    of  plants   and 

animals. 

We  saw  also  that  classification  is  not  merely  the  determina- 
tion of  isolated  groups  of  things,  but  a  systematic  arrangement 
of  such   groups   in    relation  to  one  another.     Hence,  again, 
Definitions  are  not  independent,  but  relative  to  one  another ; 
and,  of  course,  in  the  same  way  as  classes  are  relative.     That 
is  to  say,  as  a  class  is  placed  in  subordination  to  higher  or 
more  comprehensive  groups,  so  the  definition  of  its  name  is 
subordinate  to  that  of  their  names  ;  and  as  a  class  stands  in 
contrast  with  co-ordinate  classes  (those  that  are  in  the  same 
degree  of   subordination  to  the  same  higher  groups),  so  the 
definition  of  its  name  is  in  contrast  or  co-ordination  with  the 
definitions  of  their  names. 

Lion  is  subordinate  to  Felis.  to  Digitigrade,  to  Carnivore  and  so  on  up 


NOMENCLATURE 


275 

to  Animal;  and    beyond  the  Animal  Kingdom,  to  Phenomenon  :  it  is 

wi'th  A""      r'V  JZ^'J"""^'  ''''  '  ^"^  "^^^^  ^^^°^^Jy  i^  i^  co-ordinate 

w   h  Felf;  K^:\Z"'''  "^^f  '°"^  ""'^^  '^^'-"^  ^--  co-ordinate 
wi  h  Fehs.     The  definition  of  Lion,  therefore,  is  subordinate  to  that  of 

Fehs.  and  to  all  above  it  up  to  Phenomenon;  and  is  co-ordinate  with 

fl      ^T"'  t  .""'i^  ^^^  'P"'^"^  ^^  '^^  ^^"^^  g^^d^-    This  is  the  ground 
of  the  old  method  of  Definition  per  gams  et  diffemitiam. 

The  Genus  being  the  next  class  above  any  Species,  the  differentia  or 

Difference  consists  of  the  qualities  which  mark  that  Species  in  addition 

to  those  that  mark  the  Genus,  and  which  therefore  distinguish  it  from 

all  other  Species  of  the  same  Genus.      In  the  above  definition  of  Lion 

for  example,  all  the  properties  down  to  "light  and  muscular  in  build'' 

are  generic  that  is.  are  possessed  by  the  whole  Genus.  Felis;  and  the 

remaining  four  (size,  colour,  tufted  tail,  and  mane  in  the  male)  are  the 

Difference  or  specific  properties,  because  in  those  points  the  Lion  con- 

Tw7'l\'^^   °'^"'   ^P""^"^   ^^  '^^'   Genus.     Differences   may   be 
exhibited  thus :  ^ 


Lion. 
Size  :   about  9I  feet  from  nose  to 

tip  of  tail. 
Colour  :  tawny. 
Tail  :  tufted  in  the  male. 
Mane  :  present  in  the  male. 


Tiger. 


About  10  feet. 

Warm  tawny,  striped  with  black. 

Tapering. 

Both  sexes  maneless. 


There  are  other  differences  in  the  shape  of  the  skull.    In  defining  Lion 
then.    It   would   have   been   enough   to   mention   the   Genus   and   the 
properties  making  up  the  Difference  ;    because  the  properties  of  the 
Genus  may  be  found  by  turning  to  the  definition  of  the  Genus  :  and  on 
the  principle  of  economy,  whatever  it  is  enough  to  do  it  is  right  to  do 
To  define  ;  by  genus  and  difference.'  then,  is  a  point  of  elegance,  when 
the  genus  is  known  ;  but  the  only  way  of  knowing  it  is  to  compare  the 
individuals  comprised  in  it  and  in  co-ordinate  genera,  according  to  the 
methods  of  scientific   classification.      It   may  be  added  that,  as  the 
genus  represents  ancestral  derivation,   the  predication  of  genus  in  a 
definition  indicates  the  remote  causes  of  the  phenomena  denoted  by  the 
name  defined.     And  this  way  of  defining  corresponds  with  the  method 
of  double  naming  by  genus  and  species  :  Felis  ho,  Felis  tigris,  etc. ;   Vanessa 
Atalanta,  Vanessa  lo,  etc. 

The  so-called  Genetic  Definition,  chiefly  used  in  Mathematics,  is 
a  rule  for  constructing  that  which  a  name  denotes,  in  such  a  way  as  to 
ensure  Its  possessing  the  primary  attributes  connected  by  the  name 
itius.  for  a  circle  :  Take  any  point  and.  at  any  constant  distance  from 
It.  trace  a  line  returning  into  itself.  In  Chemistry  a  genetic  definition 
ot  any  compound  might  be  given  in  the  form  of  directions  for  the 
requisite  synthesis  of  elements. 


276      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

§  6.  The  difficulties  and  limits  of  Definition  must  next  be 
considered.     The  chief  difficulty  in  the  definition  of  scientific 
names  consists  in  determining  exactly  the  nature  of  the  thmgs 
denoted  by  them,  as  in  classifying  plants  and  animals.   If  organic 
species  are  free  growths,  continually  changing,  however  gradually, 
according  as  circumstances  give  some  advantage  to  one  form 
over  others,  we  may  expect  to  find  such  species  branching  mto 
varieties,  which  differ  considerably  from  one  another  in  some 
respects,  though   not   enough   to   constitute  distinct  species. 
This  is  found  to  be  the  case ;  and,  consequently,  there  arises 
some  uncertainty  in  collecting  from  all  the  varieties  those  attri- 
butes which  are  common  to  the  species  as  a  whole ;  and,  there- 
fore, of  course,  uncertainty  in  defining  the  species.     The  same 
difficulty  may  occur  in  defining  a  genus,  on  account  of  the 
extent  to  which  some  of  its  species  differ  from  others,  whilst 
having  enough  of  the  common  character  to  deter  the  classifier 
from  forming  a  distinct  genus  on  their  account.     On  the  other 
hand,  the  occurrence  of  numerous  intermediate  varieties  may 
make  it  difficult  to  distinguish  genera  or  species  at  all.     Even 
the  Kingdoms  of  plants  and  animals  cannot  be  precisely  dis- 
criminated :  sponges  and  other  organisms  seeming  to  belong  to 
one  as  much  as  to  the  other.     Now,  where  there  is  a  difficulty 
of  classification  there  must  be  a   corresponding   difficulty  of 

definition. 

It  has  been  proposed  in  such  cases  to  substitute  a  Type  for  a  Defini- 
tion •  to  select  some  variety  of  a  species,  or   species  of  a  genus,  as 
exhibiting  its  character  in  an  eminent  degree,  and  to  regard  other  groups 
as  belonging  to  the  same  species  or  genus,  according  as  they  agree 
more  with  this  Type  than  with  other  Types  representing  other  species 
or  genera.     But  the  selection  of  one  group  as  typical  implies  a  recog- 
nition of  its  attributes  as  generally  prevailing  (though  not  universally) 
throughout  the  species  or  genus  ;  and  to  recognise  these  attributes  and 
yet  refuse  to  enumerate  them  in  a  Definition,  seems  to  be  no  great  gain. 
To  enumerate  the  attributes  of  the  Type  as  an  Approximate  Definition 
of  the  species  or  genus,  true  of  most  of  the  groups  constituting  the 
species  or  genus,  answers  the  same  purpose,  is  more  explicit,  and  can 
mislead  no  one  who  really  attends  to  the  exposition.     An  Approximate 
Definition  is,  indeed,  less  misleading  than  the  indication  of  a  Type  ;  for 
the  latter  method  seems  to  imply  that  the  group  which  is  now  typical 


NOMENCLATURE  277 

has  a  greater  permanence  or  reality  than  its  co-ordinate  groups; 
whereas,  for  aught  we  know,  one  of  the  outside  varieties  or  species 
may  even  now  be  superseding  and  extinguishing  it.  But  the  statement 
of  a  Definition  as  approximate,  is  an  honest  confession  that  both  the 
definition  and  the  classification  are  (like  a  provisional  hypothesis)  merely 
the  best  account  we  can  give  of  the  matter  according  to  our  present 
knowledge. 

§  7-  The  limits  of  Definition  are  twofold  :  (a)  A  name  whose 
meaning  cannot  be  analysed  cannot  be  defined.  This  limita- 
tion meets  us  only  in  dealing  with  the  names  of  the  metaphy- 
sical parts  or  simple  qualities  of  objects  under  the  second 
requisite  of  a  Terminology. 

Resistance  and  weight,  colour  and  its  modes,  many  names  of  sounds, 
tastes,  smells,  heat  and  cold— in  fact,  whatever  stands  for  an  unanalys- 
able perception,  cannot  be  made  intelligible  to  any  one  who  has  not 
had  experience  of  the  facts  denoted  ;  they  cannot  be  defined,  but  only 
exemplified.  A  sort  of  genetic  definition  may  perhaps  be  attempted,  as 
if  we  say  that  colour  is  the  special  sensation  of  the  retina,  or  that 
blue  is  the  sensation  produced  by  a  ray  of  light  vibrating  about 
700.000,000,000,000  times  a  second  ;  but  such  expressions  can  give  no 
notion  of  our  meaning  to  a  blind  man,  or  to  any  one  who  has  never 
seen  a  blue  object.  Nor  can  we  explain  what  heat  is  like,  or  the  smell 
of  tobacco,  to  those  who  have  never  experienced  them ;  nor  the  sound 
of  C  128  to  one  who  knows  nothing  of  the  musical  scale. 

If,  however,  we  distinguish  the  property  of  an  object  from  the 
sensation  it  excites  in  us,  we  may  define  any  simple  property  as  '  the 
power  of  producing  the  sensation  ' ;  the  colour  of  a  flower  as  the  power 
of  exciting  the  sensation  of  colour  in  us.  Still,  this  gives  no  information 
to  the  blind  nor  to  the  colour-blind. 

(d)  The  second  limit  of  Definition  is  the  impossibility  of 
exhausting  infinity,  which  would  be  necessary  in  order  to  convey 
the  meaning  of  the  name  of  any  individual  thing  or  person. 

For,  as  we  saw  in  ch.  iv.,  if  in  attempting  to  define  a  proper  name  we 
stop  short  of  infinity,  our  list  of  qualities  or  properties  may  possibly  be 
found  in  two  individuals,  and  then  it  becomes  the  definition  of  a  class- 
name,  or  general  name,  however  small  the  actual  class.  Hence  we  can 
only  give  a  Description  of  that  which  a  proper  name  denotes,  enume- 
rating enough  of  its  properties  to  distinguish  it  from  everything  else  as 
far  as  our  knowledge  goes. 

Abstract  names  may  be  defined  by  defining  the  corresponding 
concrete:  the  definition  of  'human  nature'  is  the  same  as  of  'man.' 


278      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

But  if  the  corresponding  concrete  be  a  simple  sensation  (as  blue),  this 
being  indefinable,  the  abstract  (blueness)  is  also  indefinable. 

§  8.  The  five  Predicables  (Species,  Genus,  Difference,  Pro- 
prium.  Accident)  may  best  be  discussed  in  connection  with 
Classification  and  Definition;  and  in  giving  an  account  of 
Classification,  most  of  what  has  to  be  said  about  them  has 
been  anticipated.  Their  name  indeed  connects  them  with  the 
doctrine  of  Propositions ;  for  Predicables  are  terms  that  may 
be  predicated,  classified  according  to  their  connotative  relation 
to  the  Subject  of  a  proposition  (that  is,  according  to  the  relation 
in  which  their  connotation  stands  to  the  connotation  of  the 
Subject) ;  nevertheless,  the  significance  of  the  relations  of  such 
predicates  to  a  subject  is  derivative  from  the  general  doctrine 
of  classification. 

For  example,  in  the  proposition  'X  is  Y,'  Y  must  be  one  of  the  five 
sorts  of  Predicables  in  relation  to  X  ;  but  of  what  sort,  depends  upon 
what  X  (the  subject)  is,  or  means.  The  subject  of  the  proposition  must 
be  either  a  Definition,  or  a  general  Connotative  Name,  or  a  Singular 
Name. 

If  X  is  a  Definition,  Y  must  be  a  Species  ;  for  nothing  but  a  general 
name  can  be  predicated  of  a  Definition  :  and,  strictly  speaking,  it  is 
only  in  relation  to  a  Definition  (as  Subject)  that  Species  can  be  a 
predicable  ;  when  it  is  called  Species  predicabilis  (i). 

If  X  is  a  Connotative  Name,  it  is  itself  a  Species  {Species  siihjicihilis)  ;  and 
the  place  of  the  Subject  of  a  proposition  is  the  usual  one  for  Species. 
The  Predicate,  Y,  may  then  be  related  to  the  Species  in  three  different 
ways.  First,  it  may  be  a  Definition,  exactly  equivalent  to  the  Species  ; 
— in  fact,  nothing  else  than  the  Species  in  an  explicit  form,  the  analysis 
of  its  connotation.  It  seems  most  reasonable  to  regard  this  as  a  second 
form  of  the  Species  predicabilis.  Secondly,  the  Predicate  may  be,  or 
connote,  some  part  only  of  the  Definition  or  connotation  of  the  Species  ; 
and  then  it  iseither  Genus  (2),  or  Difference  (3).  Thirdly,  the  Predicate 
may  connote  no  part  of  the  Definition,  and  then  it  is  either  derivable 
from  it,  being  a  Proprium  (4),  or  not  derivable  from  it,  being  an 
Accident  (5).  These  points  of  doctrine  will  be  expanded  and  illustrated 
in  subsequent  pages. 

If  X  is  a  Singular  Name,  deriving  connotation  from  its  constituent 
terms  (chap,  i v.  §  2),  as  '  The  present  Emperor  of  China,'  it  may  be  treated 
as  a  Species  suhjicibilis.  Then  that  he  is  '  an  absolute  monarch,'  predi- 
cates a  Genus  ;  because  that  is  a  genus  of  '  Emperor  of  China,'  a  part  of 
the  Singular  Name  that  gives  it  connotation.     That  he  wecirs  a  yellow 


NOMENCLATURE 


279 


robe  is  a  Proprium,  derivable  from  the  ceremonial  of  his  court.     That 
he  is  thirty  years  of  age  is  an  Accident. 

But  if  X  is  a  Proper  Name,  having  no  connotation,  Y  must  always  be 
an  Accident ;  since  there  can  then  be  no  Definition  of  X,  and  therefore 
neither  Species,  Genus,  Difference,  nor  Proprium.  Hence,  that 
'  Alphonso  Schultze  is  a  man  '  is  an  Accidental  Proposition :  '  man  '  is 
not  here  a  Species  predicabilis ;  for  the  name  might  have  been  given  to  a 
dog  or  a  mountain.  That  is  what  enables  the  proposition  to  convey 
information:  it  would  be  useless  if  the  Proper  Name  implied 
'  humanity.' 

Species  is  most  frequently  used  (as  in  Zoology)  for  the  class  denoted 
by  a  general  name ;  but  in  Logic  it  is  often  better  to  treat  it  as  a 
general  name  used  connotatively  for  the  attributes  possessed  in  common 
by  the  things  denoted,  and  on  account  of  which  they  are  regarded  as  a 
class :  it  is  sometimes  called  the  Essence  (§  9).  In  this  connotative 
sense,  a  Species  is  implicitly  what  the  Definition  is  explicitly  ;  and 
therefore  the  two  are  always  simply  convertible.  Thus,  'A  plane 
triangle'  (Species)  is  'a  figure  enclosed  by  three  straight  lines' 
(Definition)  :  clearly  we  may  equally  say,  '  A  figure  enclosed  by  three 
straight  lines  is  a  plane  triangle.' 

A  Genus  is  also  commonly  viewed  denotatively,  as  a  class  containing 
smaller  classes,  its  species;  but  in  Logic  it  is,  again,  often  better 
to  treat  it  connotatively,  as  a  name  whose  definition  is  part  of  the 
definition  of  a  given  species. 

A  Difference  is  the  remainder  of  the  definition  of  any  species  after 
subtracting  a  given  genus.  Hence,  the  Genus  and  Difference  together 
make  up  the  Species;  whence  the  method  of  definition  per  genus  et 
differentiam  (ante,  §  5). 

It  has  already  been  mentioned,  that  whilst  in  the  classificatory 
sciences  (Botany  and  Zoology),  the  species  is  fixed  at  the  lowest  step  of 
the  classification  (varieties  not  being  reckoned  as  classes),  and  the  genus 
is  also  fixed  on  the  step  next  above  it,  in  Logic  these  predicables  are 
treated  as  moveable  up  and  down  the  ladder  :  any  lower  class  being 
species  in  relation  to  any  higher;  which  higher  class,  wherever  taken, 
thus  becomes  a  genus.  Lion  may  logically  be  regarded  as  a  species  of 
digitigrade,  or  mammal,  or  animal ;  and  then  each  of  these  is  a  genus 
as  to  lion:  or,  again,  digitigrade  may  be  regarded  as  a  species  of 
mammal,  or  mammal  as  a  species  of  animal.  The  highest  class, 
however,  is  never  a  species ;  wherefore  it  is  called  a  Summum  Genus  : 
and  the  lowest  class  is  never  a  genus ;  wherefore  it  is  called  an  Injima 
Species.  Between  these  two  any  step  may  be  either  species  or  genus, 
according  to  the  relation  to  other  classes  in  which  it  is  viewed,  and 
is  then  called  Subaltern.  The  summum  genus,  again,  may  be  viewed  in 
relation  to  a  given  universe  or  suppositio  (that  is,  any  limited  area  of 
existence  now  the  object  of  attention),  or   to  the  whole  universe.     If 


28o     LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

we  take  the  animal  kingdom  as  our  suppositio,  Animal  is  the  summum 
genus;  but  if  we  take  the  whole  universe,  'All  things'  is  the  summum 
genus. 

"  Porphyry's  tree  "  is  used  to  illustrate  this  doctrine.  It  begins  with 
a  summum  genus,  '  Substance,'  and  descends  by  adding  differences,  step 
by  step,  to  the  infima  species,  'Man.'  It  also  illustrates  Division  by 
Dichotomy. 


CORPOREAL 


INCORPOREAt 


ANIMATE 


INANIMATE 


SENSIBLE 


INSENSIBLE 


RATIONAL 


IRRATIONAL 


Socrates    Plato  ,  Anslolle 


Beginning  with  'Substance,'  as  summum  genus,  and  adding  the  differ- 
ence '  Corporeal,'  we  frame  the  species  '  Body.'  Taking  'Body'  as  the 
genus  and  adding  the  difference  '  Animate,'  we  frame  the  species 
'  Living  Body ; '  and  so  on  till  '  Man '  is  reached  ;  which  being  infima 
species,  is  only  subdivisible  into  Individuals.  But  it  should  be  noted 
that  the  division  of  Man  into  individuals  involves  a  change  of  principle: 
it  is  a  division  of  the  denotation,  not  an  increase  of  the  connota- 
tion as  in  the  earlier  steps.  Only  one  side  of  each  dichotomy  is 
followed  out :  if  the  other  side  had  been  taken  Incorporeal  Substance 
would  be  '  Spirit' ;  which  might  be  similarly  subdivided. 

Genus  and  Species,  then,  have  a  double  relation.      In  denotation  the 
Genus  includes  the  Species,  in  connotation  the  Species  includes  the 


NOMENCLATURE  281 

Genus.      Hence  the  doctrine  that   by  increasing  the  connotation  of 
a  name  you  decrease  its  denotation  :  if,  for  example,  to  the  definition  of 

lion  you  add  '  mhabiting  Africa,'  Asiatic  lions  are  no  longer  denoted 
by  It.  On  the  other  hand,  if  you  use  a  name  to  denote  objects  that  it 
did  not  formerly  apply  to,  some  of  the  connotation  must  be  dropped  • 
If,  for  example,  the  name  •  lion  '  is  used  to  include  'tigers.'  the  tufted 
tail,  mane  and  colour  can  no  longer  be  part  of  the  meaning  of  the 
word  ;  smce  tigers  have  not  these  properties. 

This  doctrine  is  logically  or  formally  true,  but  it  may  not  always  be 
true  in  tact.  It  is  logically  true  ;  because,  wherever  we  add  to  the  con- 
notation of  a  name,  it  is  possible  that  some  things  to  which  it  formerly 
applied  are  now  excluded  from  its  denotation,  though  we  may  not 
know  of  any  such  things.  Still,  as  a  matter  of  fact,  an  object  may 
be  discovered  to  have  a  property  previously  unknown,  and  this  property 
may  be  fundamental  and  co-extensive  with  the  denotation  of  its  name 
or  even  more  widely  prevalent.  The  discovery  that  the  whale  is  a 
mammal  did  not  limit  the  class  '  whale ' ;  nor  did  the  discovery  that 
lions,  dogs,  wolves,  etc.,  walk  upon  their  toes,  affect  the  application  of 
any  of  these  names.  Similarly,  the  extension  of  a  name  to  things  not 
previously  denoted  by  it.  may  not  in  fact  alter  its  definition  ;  for  the 
extension  may  be  made  on  the  very  ground  that  the  things  now  first 
denoted  by  it  have  been  found  to  have  the  properties  enumerated 
in  its  definition,  as  when  the  name  'mammal'  was  applied  to  whales, 
dolphins,  etc. 

U,  however.  '  mammal  '  had  been  formerly  understood  to  apply  only 
to  land  animals,  so  that  its  definition  included  (at  least,  popularly)  the 
quality  of  'living  on  the  land,'  this  part  of  the  connotation  was  of 
course  lost  when  the  denotation  came  to  include  certain  aquatic 
animals.  ^ 

A  Proprium  is  an  attribute  derived  from  the  definition  :  being  either 

(a)  implied  in  it.  or  deducible  from  it.  as  'having  its  three  angles  equal 
to  two  right  angles'  may  be  proved  from  the  definition  of  a  triangle  •  or 

(b)  causally  dependent  on  it.  as  being  '  dangerous  to  flocks  '  results  from 
the  nature  of  a  wolf,  and  as  '  moving  in  an  ellipse '  results  from  the 
nature  of  a  planet  in  its  relation  to  the  sun. 

An  Accident  is  a  property  accompanying  the  defining  attributes 
without  being  deducible  from  them.  The  word  suggests  that  such  a 
property  is  merely  ■  accidental,'  or  there  '  by  chance  ' ;  but,  of  course,  it 
is  not  regarded  in  that  way. 

Proprium  and  Accident  bear  the  same  relation  to  one  another 
as  Derivative  and  Empirical  Laws  :  both  Accidents  and  Empirical  Laws 
present  problems,  the  solution  of  which  consists  in  reducing  them 
respectively,  to  Propria  and  Derivative  Laws.  In  fact,  the  predication 
of  a  Proprium  is  a  Derivative  Law,  and  the  predication  of  an  Accident 
IS  an  Empirical  Law.     Thus  the  colour  of  animals  was  once  regarded  as 


282      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

an  Accident  for  which  no  reason  could  be  given  ;  but  now  the  colour  of 
animals  is  regarded  as  an  effect  of  their  nature  and  habits,  the  chief 
cause  of  it  being  the  advantage  of  concealment ;  whilst  in  other  cases, 
as  among  brightly  coloured  insects  and  snakes,  the  cause  seems  to 
be  the  advantage  of  advertising  their  own  noxiousness.  If  such 
reasoning  is  sound,  colour  is  a  Proprium  (and  if  so.  it  cannot  logi- 
cally be  included  in  a  Definition,  but  it  is  better  to  be  judicious  than 

formal).  . 

If  the  colour  of  animals  is  a  Proprium.  we  must  recognise  a  distmction 
between  Inseparable  and  Separable  Propria,  according  as  they  do,  or 
do  not,  always  accompany  the  essence:  for  mankind  is  regarded  as  one 
species ;  but  each  colour,  white,  black  or  yellow,  is  separable  from  it 
under  different  climatic  conditions:  whilst  tigers  are  everywhere 
coloured  and  striped  in  much  the  same  way  ;  so  that  we  may  consider 
their  colouring  as  inseparable,  in  spite  of  exceptional  specimens  black 

or  white.  . 

The  same  distinction  may  be  drawn  between  Accidents.  '  Inhabiting 
Asia '  is  an  Inseparable  Accident  of  tiger,  but  a  Separable  Accident  of 
lion.  Even  the  occasional  characteristics  and  occupations  of  individuals 
are  sometimes  called  Separable  Accidents  of  the  species;  as,  of  Man, 
being  colour-blind,  carpentering,  or  running. 

A  Proprium  in  the  original  signification  of  the  term  {'iSiop)  was 
peculiar  to  a  Species,  never  found  with  any  other,  and  was  therefore 
convertible    with    the    Subject;     but    this    restriction    is    no    longer 

insisted  on.  ■       -.r    u  i 

§  9.  Any  predication  of  a  Genus,  Difference  or  Definition,  is  a  Verbal, 
Analytic,  or  Essential  proposition:  and  any  predication  of  a  Proprium 
or  Accident,  is  a  Real,  Synthetic,  or  Accidental  proposition  (chap.  v.  §  6). 
A  Proposition  is  called  Verbal  or  Analytic  when  the  predicate  is  a  part, 
or  the  whole,  of  the  meaning  of  the  subject;  and  of  course,  the  subject 
being  species,  a  genus  or  difference  is  part,  and  a  definition  is  the  whole, 
of  its  meaning  or  connotation.  Hence  such  a  proposition  has  also  been 
called  explicative.  Again,  a  proposition  is  called  Real  or  Synthetic 
when  the  predicate  is  no  part  of  the  meaning  of  the  subject;  and, 
the  subject  being  species,  a  proprium  or  accident  is  no  part  of  its 
meaning  or  connotation.     Hence  such  a  proposition  has  been  called 

ampliative. 

As  to  Essential  and  Accidental,  these  terms  are  derived  from  the 
doctrine  of  Realism.  Realists  maintain  that  the  Essence  of  a  thing,  or 
that  which  makes  a  thing  to  be  what  (or  of  what  kind)  it  is,  also  makes 
everything  else  of  the  same  kind  to  be  what  it  is.  The  Essence,  they 
say,  is  not  proper  to  each  thing  or  separately  inherent  in  it,  but  is  an 
•Universal'  common  to  all  things  of  that  kind.  Some  hold  that  the 
universal  nature  of  things  of  any  kind  is  an  Idea  existing  apart  from 
them  in  the  intelligible  world,  a  rather  shy  corner,  invisible  to  mortal 


NOMENCLATURE 


283 


eye  and  only  accessible  to  thought ;  whence  they  are  called  noumena : 
that  only  the  Idea  is  truly  real,  and  that  the  things  (say,  men,  lions, 
bedsteads  and  cities)  which  appear  to  us  in  sense-perception,  and 
which  therefore  are  called  phenomena,  only  exist  by  participating  in. 
or  imitating,  the  idea  of  each  kind  of  them.  The  standard  of  this  school 
bears  the  legend  Ufiiversalia  ante  rem. 

But  others  think  that  the  Universal  does  not  exist  apart  from  particular 
things,  but  is  their  present  Essence;  gives  them  actuality  as  individual 
substances;  "informs"  them,  or  is  their  formal  cause,  and  makes  them 
to  be  what  they  are  of  their  kind  according  to  the  definition:  the 
universal  lion  is  in  all  lions,  and  is  not  merely  similar,  but  identical  in 
all;  for  thus  the  Universal  Reason  thinks  and  energises  in  Nature. 
This  school  inscribes  upon  its  banners,  Universalia  in  re. 

To  define  anything,  then,  is  to  discover  its  Essence,  whether  tran- 
scendent or  immanent;  and  to  predicate  the  definition,  or  any  part  of 
it  (genus  or  difference),  is  to  enounce  an  essential  proposition.  But  a 
proprium,  being  no  part  of  a  definition,  though  it  always  goes  along 
with  it,  does  not  show  what  a  thing  is ;  nor  of  course  does  an  accident ; 
so  that  to  predicate  either  of  these  is  to  enounce  an  accidental 
proposition. 

Another  school  of  Metaphysicians  denies  the  existence  of  Universal 
Ideas  or  Forms  ;  the  real  things,  according  to  them,  are  individuals ; 
which,  so  far  as  any  of  them  resemble  one  another,  are  regarded  as 
forming  classes;  and  the  only  Universal  is  the  class-name,  which  is 
applied  universally  in  the  same  sense.  Hence,  they  are  called  Nominalists. 
The  sense  in  which  the  name  is  applied,  is  derived,  they  say,  from  a 
comparison  of  the  individuals,  and  by  abstraction  of  the  properties  they 
have  in  common ;  and  thus  the  definition  is  formed.  Universalia  post 
rem  is  their  motto.  Some  Nominalists,  however,  hold  that,  though 
Universals  do  not  exist  in  nature,  they  do  in  our  minds,  as  Abstract 
Ideas  or  Concepts ;  and  that  to  define  a  term  is  to  analyse  the  Concept 
it  stands  for;  whence,  these  philosophers  are  called  Conceptualists. 

Such  questions  belong  to  Metaphysics  and  Psychology  rather  than  to 
Logic ;  and  I  have  only  given  a  commonplace  account  of  a  subject  upon 
every  point  of  which  there  is  much  difference  of  opinion. 

§  10.  The  doctrine  of  the  Predicaments,  or  Categories,  is  so  inter- 
woven with  the  history  of  speculation  and  especially  of  Logic  that, 
though  its  vitality  is  exhausted,  it  can  hardly  be  passed  over  unmen- 
tioned.  The  Predicaments  of  Aristotle  are  the  heads  of  a  classification 
of  terms  as  possible  predicates  of  a  particular  thing  or  individual. 
Hamilton  {Logic :  Lect.  xi.)  has  given  a  classification  of  them;  which, 
if  it  cannot  be  found  in  Aristotle,  is  an  aid  to  the  memory,  and  may  be 
thrown  into  a  table  thus  {cf.  Bain :  Logic,  App.  C.) : 


284      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 


Substance 

ovffla 

(I) 

-Quantity 

TTOffOU 

{2) 

[Attribute] 

-Quality 

TTOIOV 

(3) 

-Relation 

irpdff  TL 

(4) 

rWhere 
-When 

irov 

(5) 

irdre 

(6) 

pAction 

TTOie^V 

(7) 

[Modes  of  Relation]     _^ 

"^                                     LPassion 

irdax^iv 

(8) 

pPosture 

Keiadai 

(9) 

LHabit 

h,€iv 

(lO) 

Taking  a  particular  thing  or  individual,  as  'Socrates,'  this  is  Substance 
in  the  proper  sense  of  the  word,  and  can  never  be  a  predicate,  but  is  the 
subject  of  all  predicates.  We  may  assert  of  him  (i)  Substance  in  the 
secondary  sense  (species  or  genus)  that  he  is  a  man  or  an  animal ; 
(2)  Quantity,  of  such  a  height  or  weight ;  (3)  Quality,  fair  or  dark ; 
(4)  Relation,  shorter  or  taller  than  Xanthippe  ;  (5)  Where,  at  Athens ; 
(6)  When,  two  thousand  and  odd  years  ago;  (7)  Action,  that  he  questions 
or  exercises  ;  (8)  Passion,  that  he  is  answered  or  condemned ;  (9)  Posture, 
that  he  sits  or  stands  ;  (10)  Habit,  that  he  is  clothed  or  armed. 

Thus  illustrated  {Categoric:  c.  4),  the  Predicaments  seem  to  be  a  list 
of  topics,  generally  useful  for  the  analysis  and  description  of  an 
individual,  but  wanting  in  the  scientific  qualities  of  rational  arrange- 
ment, derivation  and  limitation.  Why  are  there  just  these  heads,  and 
just  so  many  ?  It  has  been  suggested  that  they  were  determined  by 
grammatical  forms :  for  Substance  is  expressed  by  a  substantive ; 
Quantity,  Quality  and  Relation  are  adjectival;  Where  and  When, 
adverbial ;  and  the  remaining  four  are  verbal.  It  is  true  that  the  parts 
of  speech  were  not  systematically  discriminated  until  some  years  after 
Aristotle's  time;  but,  as  they  existed,  they  may  have  unconsciously 
influenced  his  selection  and  arrangement  of  the  Predicaments.  Where 
a  principle  is  so  obscure  one  feels  glad  of  any  clue  to  it  {cf.  Grote's 
Aristotle,  c.  3,  and  Zeller's  .^Ws/o//^,  c.  6).  But  whatever  the  origin 
and  original  meaning  of  the  Predicaments,  they  were  for  a  long  time 
regarded  as  a  classification  of  things ;  and  it  is  in  this  sense  that  Mill 
criticises  them  {Logic  :  Bk.  I.  c   3). 

If,  however,  the  Predicaments  are  heads  of  a  classification  of  terms 
predicable,  we  may  expect  to  find  some  connection  with  the  Pre- 
dicables  ;  and,  in  fact,  secondary  Substances  are  species  and  genus; 
whilst  the  remaining  nine  forms  are  generally  accidents.  But,  again, 
we  may  expect  some  agreement  between  them  and  the  fundamental 
forms  of  predication  {ante,  chap.  i.  §  5,  and  chap.  ii.  §  4) :  Substance, 
whether  as  the  foundation  of  attributes,  or  as  genus  and  species,  implies 
the  predication  of  coinherence,  which  is  one  mode  of  Co-existence. 
Quantity  is  predicated  as  equality  (or  inequality)  a  mode  of  Likeness  ; 


NOMENCLATURE 


285 


and  the  other  mode  of  Likeness  is  involved  in  the  predication  of 
Quality.  Relation,  indeed,  is  the  abstract  of  all  predication,  and  ought 
not  to  appear  in  a  list  along  with  special  forms  of  itself.  '  Where '  is 
position,  or  Co-existence  in  space  ;  and  '  When  '  is  position  in  time, 
or  Succession.  Action  and  Passion  are  the  most  interesting  aspect  of 
Causation.  Posture  and  Habit  are  complex  modes  of  Co-existence,  but 
too  specialised  to  have  any  philosophic  value.  Now,  1  do  not  pretend 
that  this  is  what  Aristotle  meant  and  was  trying  to  say :  but  if  Like- 
ness, Co-existence,  Succession  and  Causation  are  fundamental  forms  of 
predication,  a  good  mind  in  analysing  the  fact  of  predication  is  likely  to 
happen  upon  them  in  one  set  of  words  or  another. 

By  Kant  the  word  Category  has  been  appropriated  to  the  highest 
forms  of  judgment,  such  as  Unity,  Reality,  Substance  and  Cause, 
under  which  the  Understanding  reduces  phenomena  to  order  and 
thereby  constitutes  Nature.  This  change  of  meaning  has  not  been 
made  without  a  certain  continuity  of  thought ;  for  forms  of  judgment 
are  modes  of  predication.  But,  besides  altering  the  list  of  Categories 
and  greatly  improving  it,  Kant  has  brought  forward  under  an  old  title 
a  doctrine  so  original  and  suggestive  that  it  has  extensively  influenced 
the  subsequent  history  of  Philosophy.  At  the  same  time,  and  pro- 
bably as  a  result  of  the  vogue  of  the  Kantian  philosophy,  the  word 
'  category'  has  been  vulgarised  as  a  synonym  for  '  class,'  just  as  '  pre- 
dicament '  long  ago  passed  from  Scholastic  Logic  into  common  use  as  a 
synonym  for  'plight.'  A  minister  is  said  to  be  '  in  a  predicament,' 
or  to  fall  under  the  '  category  of  impostors.' 


CHAPTER  XXIII 
DEFINITION  OF  COMMON  TERMS 

§  I.  Ordinary  words  may  need  definition,  if  in  the  course  of 
exposition  or  argument  their  meaning  is  liable  to  be  mistaken. 
Definition  should  not  be  regarded  as  giving  the  sense  of  the 
word  for  all  occasions  of  its  use.  It  is  an  operation  of  great 
delicacy.  Fixity  of  meaning  in  the  use  of  single  words  is 
contrary  to  the  genius  of  the  common  vocabulary;  since 
each  word,  whilst  having  a  certain  predominant  character, 
must  be  used  with  many  shades  of  significance,  in  order  to 
express  the  different  thoughts  and  feelings  of  multitudes  of 
men  in  endlessly  diversified  situations ;  and  its  force,  when- 
ever it  is  used,  is  qualified  by  the  other  words  with  which  it 
is  connected  in  a  sentence,  by  its  place  in  the  construction 
of  the  sentence,  by  the  emphasis,  or  by  the  pitch  of  its 
pronunciation  compared  with  the  other  words. 

Clearly,  the  requisite  of  a  scientific  language,  *that  every 
word  shall  have  one  meaning  well  defined,'  is  too  exacting 
for  popular  language;  because  tlie  other  chief  requisite  of 
scientific  language  cannot  be  complied  with,  'that  there  be 
no  important  meaning  without  a  name.'  'Important  mean- 
ings,' or  what  seem  such,  are  too  numerous  to  be  thus 
provided  for ;  and  new  ones  are  constantly  arising,  as  each 
of  us  pursues  his  business  or  his  pleasure,  his  meditations 
or  the  excursions  of  his  fancy.  It  is  impossible  to  have  a 
separate  term  for  each  meaning:  and,  therefore,  the  terms 
we  have  must  admit  of  variable  application. 

An  attempt  to  introduce  new  words  is  generally  disgusting. 


DEFINITION    OF   COMMON   TERMS  287 

Few  men  have  mastered  the  uses  of  half  the  words  already  to 
be  found  in  our  classics.  Much  more  would  be  lost  than 
gained  by  doubling  the  dictionary.  It  is  true  that,  at  certain 
stages  in  the  growth  of  a  people,  a  need  may  be  widely  felt  for 
the  adoption  of  new  words :  such,  in  our  own  case,  was  the 
period  of  the  Tudors  and  early  Stuarts.  Many  fresh  words, 
chiefly  from  the  Latin,  then  appeared  in  books,  were  often 
received  with  reprobation  and  derision,  sometimes  disappeared 
again,  sometimes  established  their  footing  in  the  language. 
See  The  Art  of  Eiiglish  Poetry  (ascribed  to  Puttenham), 
Book  III.  chap.  4,  and  Ben  Jonson's  Poetaster,  Act  v.  sc.  i. 
Good  judges  did  not  know  whether  a  word  was  really  called 
for  :  even  Shakespeare  thought '  remuneration  '  and  '  accommo- 
date '  ridiculous.  But  such  national  exigencies  rarely  arise  • 
and  in  our  own  time  great  authors  distinguish  themselves  by 
the  plastic  power  with  which  they  make  common  words  convey 
uncommon  meanings. 

Fluid,  however,  as  the  ordinary  language  is  and  ought  to 
be,  it  may  be  necessary  for  the  sake  of  clear  exposition,  or 
to  steady  the  course  of  an  argument,  to  avoid  either  sophistry 
or  unintentional  confusion,  that  words  should  be  defined  and 
discriminated ;  and  we  must  discuss  the  means  of  doing  so. 

§  2.  Scientific  method  is  applicable,  with  some  qualifications, 
to  the  definition  of  ordinary  words.  Classification  is  involved 
in  any  problem  of  definition  :  at  least,  if  our  object  is  to  find 
a  meaning  that  shall  be  generally  acceptable  and  intelligible. 
No  doubt  two  disputants  may,  for  their  own  satisfaction,  adopt 
any  arbitrary  definition  of  a  word  important  in  their  contro- 
versy ;  or  any  one  may  define  a  word  as  he  pleases,  at  the  risk 
of  being  misunderstood,  provided  he  has  no  fraudulent  in- 
tention. But  in  exposition  or  argument  addressed  to  the 
public,  where  words  are  used  in  some  of  their  ordinary  senses, 
it  should  be  recognised  that  the  meaning  of  each  one  involves 
that  of  many  others.  For  language  has  grown  with  the  human 
mind,  as  representing  its  knowledge  of  the  world :  this  know- 
ledge consists  of  the  resemblances  and  differences  of  things 


288      LOGIC:    DEDUCTIVE    AND   INDUCTIVE 

and  activities,  that  is,  of  classes  and  causes ;  and  as  there  is 
such  order  in  the  world,  so  there  must  be  in  language: 
language,  therefore,  embodies  an  irregular  classification  of 
things  with  their  attributes  and  relations  according  to  our 
knowledge  and  beliefs.  The  best  attempt  (known  to  me) 
to  carry  out  this  view  is  contained  in  Roget's  Thesaurus^ 
which  is  a  classification  of  English  words  according  to  their 
meaning :  founded,  as  the  author  tells  us,  on  the  models  of 
Zoology  and  Botany. 

Popular  language,  indeed,  having  grown  up  with  a  predominantly 
practical  purpose,  represents  a  very  imperfect  classification  philoso- 
phically considered.  Things,  or  aspects,  or  processes  of  things,  that 
have  excited  little  interest,  have  often  gone  unnamed  ;  so  that  scientific 
discoverers  are  obliged,  for  scientific  purposes,  to  invent  thousands  of 
new  names.  Strong  interests,  on  the  other  hand,  give  such  a  colour  to 
words  that,  where  they  enter,  it  is  difficult  to  find  any  indifferent  expres- 
sions. Consistency  being  much  prized,  though  often  the  part  of  a  block- 
head, inconsistency  implies  not  merely  the  absence  of  the  supposed 
virtue,  but  a  positive  vice :  Beauty  being  attractive  and  ngline'is  the 
reverse,  if  we  invent  a  word  for  that  which  is  neither,  '  plainness,'  it  at 
once  becomes  tinged  with  the  ugly,  In  short,  we  love  beauty  and 
morality  so  much  as  to  be  almost  incapable  of  signifying  their  absence 
without  expressing  aversion. 

Again,  the  erroneous  theories  of  mankind  have  often  found  their  way 
into  popular  speech,  and  their  terms  have  remained  there  long  after  the 
rejection  of  the  beliefs  they  embodied  :  as — lunatic,  augury,  divination, 
spell,  exorcism :  though,  to  be  sure,  such  words  may  often  be  turned  to 
good  account,  besides  the  interest  of  preserving  their  original  sense. 
Language  is  a  record  as  well  as  an  index. 

Language,  then,  being  essentially  classificatory,  any  attempt 

to  ascertain  the  meaning  of  a  word,  far  from  neglecting  its 

relations   to   others,   should   be   directed   toward   elucidating 

them. 

Every  word  belongs  to  a  group,  and  this  group  to  some  other  larger 
group.  Groups  are  sometimes  formed  by  derivation,  at  least  so  far  as 
their  differences  are  marked  merely  by  inflections,  as  ihort,  shorter, 
shorten,  shortly :  but,  for  the  most  part,  are  a  conflux  of  words  from 
many  different  sources.  Repose,  depose,  suppose,  impose,  propose,  are  not 
nearly  connected  in  meaning  ;  but  are  severally  allied  in  sense  much 
more  closely  with  words  philologically  remote.  Thus  repose  is  allied 
with  rest,  sleep,  tranquillity ;  disturbance,  unrest,  tumult:  whilst  depose  is,  in 


DEFINITION   OF  COMMON  TERMS         289 

fcTTnd 'if '"',,:"*  """"'"""■  '"""■«•  *''"""«■•  '■"'""■  confirm,  cstab- 
hsh.  and   m  another  sense,  with  ««„,««„/.  «,w, /.ot,,  ct       GrouDS 

denotd  "  '""^  resemblance  in  character  of  the  things 

Words,  accordingly,  stand  related  to  one  another,  for  the 
most  part,  though  very  irregularly,  as  genus,  species,  and 
co-ordinate  species. 

coIrfinftltvHh'  '  ^'""''  r  ''"^■'  "^  ^P^^"^  °f  "•  "'°"«''  "°'  --ctly 
(reposeofmind     ,    r  /'"?"''=■••  """^-^''-V   with  a   mental   differentia 

As  this   illustration   suggests,   synonyms  are   species    or    v;,riP(,P= 

ttmTeTu^tlttr/tr  '^  '"^^'^^  -  '''-     -"o^discri" 
T.^Z  T  ,        "'^  ^"""'"^  '"<'^"'"S  •  f"'  which  there  may  or 

^huL  -*'■  "^  ^>"°"y"'s  :  but,  if  we  attend  to  the  ways  ir^ 

wh.ch  they  are  actually  used,  perhaps  none  of  them  can  claim  To  i  a 
Senus  m  relation  to  the  rest.  If  not.  we  must  resort  to  a'ompound 
term  for  the  genus,  such  as  •  absence  of  some  sort  of  difference  Then 
«  ts  absence  of  difference  in  quantity  ;  sa.e.uss  is  of^n  absence 
of  difference  m  quality,  though  the  usage  is  not  strict:  likeness  siMv 
and  nsemMance^n  their  actual  use,  perhaps,  cannot  be  diSiminated 
unless  kkeness  be  the  more  concrete,  siJanty  the  more  abs7rait  bui 
^ey  may  all  be  used  compatibly  with  the  recognition  of  morro;  le 

absence  of  difference  of  ongin,  a  continuity  of  existence,  with  so  much 
sameness  from  moment  to  moment  as  is  compatible  with  changTsIn 
the  course  of  nature;  so  that  egg,  caterpillar,  chrysalis,  butterfly  may 
be  Identical  for  the  run  of  an  individual  life,  in  spite  of  differences 
inTdrat;'  '"'  ''"'"'"'^•^'  ^^  '^"'>'  ^^  ^  ^^"""S  tha't  all  the  dme  ,ie: 
Co-ordinate  Species,  when  positive,  have  the  least  contrariety     but 

ont^ra^es      Th°''"  '"k"''"''^  "^^^''^"^'  contradictories  and'fuUe 
contraries.     These  may  be  regarded  as  either  co-ordinate  genera  or  the 

.LnfrTr  T  ''''''' ''"""'  ^"'^  '^  ^  "^e^'i^-e  ^"d  contradictory 
hen  aclnay  implying  an  end  in  view),  motion  (limited  to  matter)  Z'- 
turbance  (implying  changes  from  a  state  of  calm),  tunuM.  ./f  a  i'  co- 
ordinate  species  of  «<,/-„/<,„,  and  are  therefore  co-ordinate  opp;shes  or 
contraries,  of  the  species  of  repose.  pposites,  or 

As  for  correlative  words,  like  Master  and  Slave.  Husband  and  Wife,  ele 
It  may  seem  far-fetched  to  compare  them  with  the  sexes  of  the  ^ame 
species  of  plants  or  animals  ;  but  there  is  this  resemblance  between  the 


290      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

two  cases,  that  sexual  names  are  correlative,  as  '  lioness.'  and  that  one 
sex  of  a  species,  like  a  correlative  name,  cannot  be  defined  without 
implying  the  other;  for  if  a  distinctive  attribute  of  one  sex  be  men- 
tioned.  as  the  lion's  mane,  it  is  implied  that  the  other  wants  it.  and 
apart  from  this  implication  the  species  is  not  defined  ;  just  as  the 
definition  of  '  master  '  implies  a  '  slave  '  to  obey. 

Common  words,  whilst  less  precise  than  the  terms  of  a  scientific 
nomenclature,  differ  from  them  also  in  this,  that  the  same  word  may 
occur  in  different  genera.  Thus,  sleep  is  a  species  of  repose  as  above, 
but  it  is  also  a  species  of  unconsciousness,  with  co-ordinate  species  swoon, 
hypnotic  state,  etc.  In  fact,  every  word  stands  under  as  many  distinct 
genera,  at  least,  as  there  are  simple  or  indefinable  qualities  to  be 
enumerated  in  its  definition. 

§  3.  But  besides  being  partly  similar  to  a  scientific  nomen- 
clature, ordinary  language  is,  of  course,  partly  a  terminology  for 
describing  things  according  to  their  qualities  and  structure.  Such 
are  all  the  names  of  colours,  sounds,  tastes,  contrasts  of  tem- 
perature, of  hardness,  of  pleasantness  ;  in  short,  all  descriptive 
adjectives,   and   al^.    names   for   the   parts   and    processes    of 
things.     Any  word  connoting  a  quality  may  be  used  to  describe 
many  very  different   things,    as   long   as   they  agree   in    this 
quality.     This  is  the  generality  of  a  word  (sometimes  said 
to  make  it,  or  its  meaning,  universal,  chap.  xxii.  §  9),  or  its 
general  applicability. 

But  we  must  observe,  that  the  quality  connoted  by  a  word,  and 
treated  as  always  the  same  quality,  is  often  only  analogically  the  same 
Take  the  word  great :  we  speak  of  a  great  storm,  a  great  man,  a  great 
book  ;  but  great  is  in  each  case  not  only  relative,  implying  small,  and 
leaving  open  the  possibility  that  what  we  call  great  is  still  smaller 
than  something  else  of  its  kind,  but  it  is  also  predicated  with  reference 
to  some  quality  or  qualities  which  may  be  very  different  in  the  several 
cases  of  its   application.     If  the   book   is   prized  for  wisdom,  or  for 
imagination,   its  greatness   lies   in   that   quality;   if  the   man   is  dis- 
tinguished for  influence,  or  for  courage,  his  greatness  is  of  that  nature  ; 
if  the  storm  is  remarkable  for  violence,  or  for  duration,  its  greatness 
depends  on  that  fact.     The  word  great,  therefore,  is  not  used  for  these 
things    in    the    same    sense,   but    only   analogically   and   elliptically. 
Similarly  with  good,  pure,  free,  strong,  rich,  and  so  on.     'Rest'  has 
not  the  same  meaning  in  respect  of  a  stone  and  of   an  animal,  nor 
•  strong  '  in  respect  of  thought  and  muscle,  nor  '  sweet '  in  respect  of 
sugar  and  music.     But  here  we  come  to  the  border  between  literal  and 


DEFINITION   OF  COMMON   TERMS  29,- 

A  Jin   1  y ''*^"''"™  "^e  may  become  literal. 

4r;  r/esS  T„7:oi;:fetb''r "'  -'-''''■  --  ^-^^^ 

scape,  or   in   defining^n/ spedrte"  m       t'^"  "r^"' "  '  '^"''■ 
doctrine,  that anvconnrf.fP,h  T'      ^'"^  '^  '^^  «™se  of  the 

it  maya   lea  t  be  co^s[dl^^t^™"''"'°'«™'^^^'"''^^°^"°i^'«^sals: 
to  sa];,   thaTln^bj^cf ;    tl 
(who,  to  fully  comprehend"  mu'cas.ivTt"„r^'''  '°  '  'f"""'"^ 

represents  a  cLsist^eteTheTrof  t^:;-  "  ^^""  ^  °^-=' 
mlLs       '™""  °'  "''"«  "  <''^«""'-  "'-y  "«  g-ded  by  the  following 

(I)  Find  the  usage  of  good  modern  authors  •  that  is  las  ,h. 
define  a  word  explicitly),  consider  what  in  ^■arous  relations  th''  """^^ 

words;  and  observe  the  quahtS  in  1    h  T  'f:"'^'"^"^  '""^  "PPo^ite 

in  which  they  differ  rom'  htrLno  ed  bvth  f  '™°'''  '^"'''  '"^ 

If  civilisation  is  to  be  defin.H         i    r  ^  ^    contraries  and  opposites. 

civihsed,  of  barCus  and  :  sa™a«  •  T       f"'?'  ^'''"'''  °'  ^"''- 

civiiised  peoples  and  ^J^:'^:^:^^:::;^:^'^^"''' 

exercise  worth  attempting.      If  poetrv  is  fn  h!    i  a      ,  "  ""' 

typical  examples  of  wh'at  g'ood  crii::  'rec  gnL     s  poeTrv  Z^''  "'"^ 
them   with  examples  of  literary  prose   oratarv    l^     ^'  ""P"^ 

determined  the  characteristics  of  elch  t.nH   i,  '""":""•      "^"°g 

them  opposite  one  another  in  parable  coumn       vvf        "'""  '°  "'^"^^ 
by  this  method  a  few  impor.Lt  wo  ds  freanenti  '''  '"''  '°  '^^^"^ 

sation  will  find  his  head  tL  cleareTt     ,''rd''rvircZTbv  thr^'^^' 
much  information  which  mpv  Ko  ""  ^^i^' collect  by  the  way 

itself,  should  he  everfind  one  '  "  ^"'""''^   '^^"  "'^  '^^^-'i™ 

pr^l"ma;  re":horl:d^li':   "^   '''"'''  '^  ^-'^^  ^--.  'he 

;-« (that^,  .appX^o  S°;^t'e^;,r  suir;^!^!:^^ 
:rm:r:;nrse^er  r  ditrrzr  r'°^^  --  -^ '"" -- 

these  en  nrrlin..  '"^ . ^^^^^f "^la  of  poetry  by  a  comparison  of  it  with 
d^::ence  uTon  it?ir:  ^  ^^l'^,-'-^  o^en  e^^s  genus  and 
•  cricket  bat  •     h  f  T  :       ,  •       '"'er-penetrate,'   ■tuning-fork,' 

insS^or'  frh::^^drriX"°TndXtvt  rst  rr' 

covered,  it  is  well  to  state  it/..^„«.  .,  „p,ZZ         ''""'"°"  '''  "''■ 

(4)  In  defining   any  term  we  should   avoid   encroaching  upon    the 

meaning  of  any  of  the  co-ordinate  terms;  for  else  their  usefuCsst 


2^2      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

lessened  :  as  by  making  '  law  '  include    '  custom.'  or  '  wealth  '  include 
'labour' or  *  culture.'  . 

(5)  If  two  or  more  terms  happen  to  be  exactly  synonymous,  it  may  be 
possible  (and,  if  so.  it  is  a  service  to  the  language)  to  divert  one  of  them 
to   any   neighbouring   meaning    that   has   no   determinate    expression^ 
Thus.  Wordsworth  and  Coleridge,  at  the  beginning  of  this  century,  took 
great  pains    to  distinguish  between  Imagination  and  Fancy,   which  at 
that  time  had  become  in  common  usage  practically  equivalent ;    and 
they  sought  to  limit  '  imagination  '  to  an  order  of  poetic  effect,  which 
(they  said)   had  prevailed  during  the  Elizabethan  age,  but  had  been 
almost  lost  during  the  Gallo-classic,  and  which  it  was  their  mission  to 
restore.       Co-ordinate    terms    often     tend    to    coalesce    and    become 
synonymous,  or  one  almost  supersedes  the  other,  to  the  consequent 
impoverishment  of  our  speech.     At  present  proposition  (that  something 
is  the   fact)  has    almost  driven   out  proposal   (that   it   is   desirable   to 
co-operate  in  some  course  of  action).     Even  good  writers  and  speakers, 
by  their  own  practice,  encourage  this  confusion :  they  submit  to  Parlia- 
ment certain  '  propositions  '  (proposals  for  legislation),  or  even  make  '  a 
proposition  of  marriage.'  Definition  should  counteract  such  a  tendency. 
(6)  We  must  avoid  the  temptation  to  extend  the  denotation  of  a  word 
so  far  as  to  diminish  or  destroy  its  connotation  ;    or  to   increase   its 
connotation  so  much  as  to  render  it  no  longer  applicable  to  things 
which  it  formerly  denoted  :  we  should  neither  unduly  generalise,  nor 
unduly  specialise,  a  term.     Is  it  desirable  to  define  education  so  as  to 
include  the   '  lessons  of  experience';    or  is  it   better  to  restrict  it  as 
implying  a  personal  educator  ?     If  any  word  implies  blame  or  praise, 
we  are  apt  to  extend  it  to  everything  we  hate  or  approve.     But  co^'ard 
cannot  be  so  defined  as  to  include  all  bullies,  nor  noble  so  as  to  include 
every  honest  man,  without  some  loss  in  distinctness  of  thought. 

The  same  impulses  make  us    specialise  words;    for,  if  two  words 
express  approval,  we  wish  to  apply  both  to  whatever  we  admire  and  to 
refuse  both  to  whatever  displeases  us.     Thus,  a  man  may  resolve  to  call 
no  one  great  who  is  not  good  :  greatness,  according  to  him,  connotes 
goodness:    whence  it  follows  that   (say)  Napoleon   I.   was   not   great. 
Another  man  is  disgusted  with  greatness  :  according  to  him,  good  and 
great  are  mutually  exclusive  classes,   sheep    and  goats,  as  in   Gray's 
wretched  clench  :  "  Beneath  the  good  how  far,  yet  far  above  the  great." 
In  fact,  however,  '  good  '  and  '  great '  are  descriptive  terms,  sometimes 
applicable  to  the  same  object,  sometimes  to  different:  but  'great'  is 
the  wider  term  and  applicable  to  goodness  itself  and  also  to  badness  ; 
whereas  by  making  '  great '  connote  goodness  it  becomes  the  narrower 
term.     And,  as  we  have  seen  (§  3),  such  epithets  may  be  applicable  to 
objects  on  account  of  different  qualities  :  good  s  not  predicated  on  the 
same  ground  of  a  man  and  of  a  horse. 

(7)  In  defining  any  word,  it  is  desirable  to  bear  in  mind  its  derivation, 


DEFINITION   OF  COMMON   TERMS  293 

and  to  preserve  the  connection  of  meaning  with  its  origin  •  unless  there 
are  preponderant  reasons  for  diverting  it.  grounded  on  our  need  of  the 

other  wordT;  T''"'  """'  ^""^  '""^  '^'^'^^  ^^^^^^y  ^f  finig  a'; 
00  The  vuta  ^^"^%P"fPf  ^-  I^  i^  better  to  lean  to  the  cla  sical 
•  ^he^otnal'r  "^"  ^'    '  ^"^'^^^^^^•'    'i-P-tinent.'    -aggravating,' 

qualities,  and  each  ^^^1^:^^:!^^^:;'--^  '^^Z 

bTblrismTT'^^/t  '^"^^  '-'  ''  ^^^^  -^'-'  civili-fiorand 
some  tS  h  on7  ^  "  '"'^  ''  '''^'^'^  ^^^^^^^^^  ^^  '^  P-try. 
must  be  stirH  ''  '"1  'T'^''  ^"^  ^''""'y  "^^'^'^'^  ^hat  the  metre 
aTmLsteT  O^^^^^^^^^  rhythm  is 

as  the  essence  of  poe^r;:^^^^  re  t^^^^^^^^^^^^^ 
intensity  of  this  mood  is  requisite.     We  also  hear  that  poetry  hof  such 
a  nature  that  the  enjoyment  of  it  is  an  end  in  itself  ;lut  as  it    s  not 
maintained  that  poetry  must  be  wholly  impersuasive  or  unL  uctive 
there  seems  to  be  no  means  of  deciding  what  amount  or  prom  nence  of 
per  uasion  or  instruction  would  transfer    the  work  to   the   re'fon   o 
o  atory  or  science.     Such  cases  make  the  method  of  defining  bv  the  aid 
of  a  type  really  useful:  the  difficulty  can  hardly  be  got  over  withom 
pointing  to  typical  examples  of  each  meaning,  and  admitting  th" there 
may  be  many  divergences  and  unclassifiable  instances  on  the  border 
between  allied  meanings.  L.uiuer 

§  5-  As  science  began  from  common  knowledge,  the  terms 
of  the  common  vocabulary  have  often  been  adopted  into  the 
s  lences,  and  many  are  still  found  there :  such  as  weight,  mass 
work,   attraction,    repulsion,    diffusion,    reflection,  absorption' 
base,  salt,  and  so  forth.  ' 

In  the  more  exact  sciences,  the  vague  popular  associations  with  such 
words  IS  hardly  any  inconvenience;  since  those  who  are  addicted  to 
such  studies  do  not  expect  to  master  them  without  undergoing  special 
discipline  ;  and,  having  precisely  defined  the  terms,  they  acquire  the 
habit  of  thinking  with  them  according  to  their  assigned  significance  in 
those  investigations  to  which  they  are  appropriate.      It  is  in  the  Social 
Sciences,  especially  Economics  and   Ethics,   that  the  use  of  popular 
terminology  is  at  once  unavoidable  and  prejudicial.      For  the  suWect- 
matters.  industry  and  the  conduct  of  life,  are  every  man's  business"  and 
accordingly,  have  always  been  discussed  with  a  consciousness  of  their 


294      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

direct  practical  bearing  upon  public  and  private  interests,  and  therefore 
in  the  common  language,  in  order  that  everybody  may  as  far  as  possible 
benefit  by  whatever  light  can  be  thrown  upon  them.     It  is  true  that 
Astronomy,  Mechanics  and  Chemistry  are  of  incalculable  importance  to 
industry,  and  to  public  and  private  interests  :  still  their  application  to 
practice  is  generally  in  the  hands  of  specialists  (navigators  or  dyers), 
who  may  undergo  the  requisite  special  training  in  proportion  as  their 
share  in  any  process  requires  an  appreciation  of  its  scientific  grounds. 
But  the  saying,  that  'what  is  everybody's  business  is  nobody's,'  re- 
ceives  melancholy  illustration  from  the   popular  attitude  toward  the 
Science  of  Wealth  and  Industry.     Is  there  not  another  saying  that  *a 
man  knows  his  own  business  best '  ?     He  looks,  perhaps,  into  a  work  on 
Economics  and  sees  that  it  is  all  about  Prices,  Money,  Rent,  Wages, 
Profits.     Now,  he  has  received  and  paid  Money  all  his  life,  and  either 
received  or  paid  Rent,  Wages  and  Profits:  how,  then,  can  things  so  familiar 
need  any  explanation  ?     He  may  often  say  with   much   truth,  that  he 
has  made  more  money  than  the  author.      It  has  been  justly  observed, 
however,  that  nearly  all  uninstructed  and  traditionary  opinions  upon 
these  subjects  are  curiously  wrong.     They  are  not  merely  erroneous, 
but  perverse  and  absurd.      The  obtaining  of  instruction,  however,  has 
been  hindered   by  the  very  means   adopted    to   facilitate   it,    the   use 
of  common  language  in  a  technical  sense  ;  for  without  special  discipline 
in  the  use  of  technicalities,  the  special  meaning  of  the  terms  employed 
will   often   be   confused   with  the  vague  meanings  that   they  have  in 
ordinary  conversation  ;  and  if  their  divergence  from  ordinary  usage  is 
observed,  it  is  likely  enough  to  give  annoyance,  or  to  raise  a  laugh  at 
the  apparent  ignorance  of  the  '  theorist '  who  wrote  the  book. 

The  almost  uniform  practice  of  Economists  and  Moralists, 
however,  shows  that,  in  their  judgment,  the  good  derived  from 
writing  in  the  common  vocabulary  outweighs  the  evil;  though 
it  is  sometimes  manifest  that  they  themselves  have  been  misled 
by  extra-scientific  meanings.     To  reduce  the  evil  as  much  as 
possible,  the  following  precautions  seem  reasonable:   (i)  To 
try  to  find  and  adopt  the  central  meaning  of  the  word  (say 
Rent  or  Money)  in  its  current  or  traditionary  applications ;  so 
as  to  lessen  in  the  greater  number  of  cases  the  jar  of  conflicting 
associations.     But   if  the  central  popular  meaning  does  not 
correspond  with  the  scientific  conception  to  be  expressed,  it 
may  be  better  to  invent  a  new  term. 

(2)  To  define  the  term  with  sufficient  accuracy  to  secure  its 
clear  and  consistent  use  for  scientific  purposes. 


DEFINITION   OF  COMMON   TERMS  295 

(3)  When  a  popular  term  has  to  be  used  in  a  sense  that 
departs  from  the  ordinary  one  in  such  a  way  as  to  incur  the 
danger  of  misunderstanding,  to  qualify  it  by  some  adjunct  or 
''  interpretation-clause." 

It  must  be  confessed  that  the  first  of  these  rules  is  not  always  adhered 
to;  and.  m  the  progress  of  a  science,  as  subtler  and  more  abstract 
relations  are  discovered  amongst  the  facts,  the  meaning  of  a  term  may 
have  to  be  modified  and  shifted  further  and  further  from  its  popular 
use.  The  term  -Rent,'  for  example,  is  used  by  economists  in  such 
a  sense,  that  they  have  to  begin  the  discussion  of  the  facts  it  denotes  bv 
explaining  that  it  does  not  imply  any  actual  payment  by  one  man 
o  another.  Here,  for  most  readers,  the  meaning  they  are  accustomed 
to,  seems  already  to  have  entirely  disappeared ;  but  worse  follows  •  and 
we  ought,  therefore,  to  pity  the  sorrows  of  a  plain  man  of  common 
sense  who  sits  down  to  study  Economics  in  a  railway  carriage. 
Difficulties  may,  however,  be  largely  overcome  by  qualifying  the  term 
m  Its  various  relations,  as  produce-rents,  ground-rents,  customary 
rents,  and  so  forth.  (C/.  Dr.  Keynes'  Scope  and  Method  of  Political 
Economy,  chap.  5.)  ^      omicai 

§  6.  Definitions  affect  the  cogency  of  arguments  in  many 
ways,  whether  we  use  popular  or  scientific  language.  If  the 
definitions  of  our  terms  are  vague,  or  are  badly  abstracted 
from  the  facts  denoted,  of  course,  all  arguments  involving  these 
terms  are  inconclusive.  There  can  be  no  confidence  in 
reasonmg  with  such  terms ;  since,  if  they  are  vague,  there  is 
nothmg  to  protect  us  from  ambiguity  ;  or,  if  their  meaning  has 
been  badly  abstracted,  we  may  be  led  into  absurdity— as  if 
'  impudence '  be  defined  in  such  a  way  as  to  confound  it  with 
honesty. 

Again,  it  is  by  Definitions  that  we  can  best  distinguish 
between  \^erbal  and  Real  Propositions.  AVhether  a  term 
predicated  is  implied  in  the  definition  of  the  subject,  or  adds 
something  to  its  meaning,  deserves  our  constant  attention. 
We  often  persuade  ourselves  that  statements  are  profound  and 
important,  when,  in  fact,  they  are  mere  verbal  propositions. 
"It  is  just  to  give  every  man  his  due";  ''the  greater  good 
ought  to  be  preferred  to  the  less  " ;  such  dicta  sound  well- 
indeed,  too  well  !     lor  'a  man's  due  '  means  nothing  else  than 


296      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

what  it  is  just  to  give  him  ;  and  '  the  greater  good '  means  the 
one  that  ought  to  be  preferred  :  these,  therefore,  are  Truisms. 
The  investigation  of  a  definition  may  be  a  very  valuable  service 
to  thought ;  but,  once  found,  there  is  no  merit  in  repeating  it. 
To  put  forward  verbal  or  analytic  propositions,  or  truisms,  as 
information  (except,  of  course,  in  actually  explaining  terms  to 
pupils),  shows  that  we  are  not  thinking  what  we  say ;  for  else 
we  must  become  aware  of  our  own  emptiness.  Every  step 
forward  in  knowledge  is  expressed  in  a  Real  or  Synthetic  Pro- 
position ;  and  it  is  only  by  means  of  such  propositions  that 
information  can  be  given  (except  as  to  the  meaning  of  words) 
or  that  an  argument  or  train  of  reasoning  can  make  any 
progress. 

Opposed  to  a  truism  is  a  Contradiction  in  Terms  ;  that  is, 
the  denying  of  a  subject  something  which  it  connotes  (or  which 
belongs  to  its  definition),  or  the  affirming  of  it  something 
whose  absence  it  connotes  (or  which  is  excluded  by  its 
definition).  A  Verbal  Proposition  is  necessarily  true,  because 
it  is  tautologous  ;  a  Contradiction  in  Terms  is  necessarily 
false,  because  it  is  inconsistent.  Yet,  as  a  rhetorical  artifice, 
or  figure,  it  may  be  effective  :  that  *  the  slave  is  not  bound  to 
obey  his  master'  may  be  a  way  of  saying  that  there  ought  to  be 
no  slaves ;  that  *  property  is  theft,'  is  an  uncompromising 
assertion  of  the  communistic  ideal.  Similarly  a  Truism  may 
have  rhetorical  value  :  that  *  a  Negro  is  a  man '  has  often  been 
a  timely  reminder,  or  even  that  "a  man's  a  man."  It  is  only 
when  we  fall  into  such  contradiction  or  tautology  by  lapse  of 
thought,  by  not  fully  understanding  our  own  words,  that  it 
becomes  absurd. 

Real  Propositions  comprise  the  predication  of  Propria  and 
Accidentia.  Accidentia,  implying  (as  we  have  seen)  a  sort  of 
empirical  law,  can  only  be  established  by  direct  induction. 
But  propria  are  deduced  from  (or  rather  by  means  of)  the 
Definition  with  the  help  of  real  propositions,  and  this  is  what 
is  called  '  arguing  from  a  Definition.'  Thus,  if  increasing 
capacity  for  co-operation  is  a  specific  character  of  Civilisationj 


DEFINITION   OF  COMMON  TERMS  297 

great  wealth  may  be  considered  as  a  proprium  of  civilised  as 
compared  with  barbarous  nations.     For  co-operation  is  made 
most  effectual  by  the  division  of  labour,  and  that  this  is  the 
chief  condition   of  producing  wealth   is   a  real  proposition, 
established  both  inductively  and  deductively.     Such  arguments 
from  Definitions  concerning  concrete  facts  and  causation  of 
course,  require  verification  by  comparing  the  conclusion  with 
the  facts.     The  verification  of  this  example  is  easy,  if  we  do 
not  let  ourselves  be  misled  in  estimating  the  wealth  of  barbarians 
by  the  ostentatious   "  pearl  and  gold  "  of  kings  and  nobles 
where  99  per  cent,  of  the  people  live  in  penury  and  servitude 
1  he  wealth  of  civilisation  is  not  only  great  but  diffused,  and  in 
Its  diffusion  its  greatness  must  be  estimated. 

To  argue  from  a  Definition   may  be  a  process  of  several 
degrees  of  complexity.     The  simplest  case  is  the  establishment 
of  a  proprium  as  the  direct  consequence  of  some  connoted 
attribute,  as  in  the  above  example.     If  the  definition  has  been 
correctly  abstracted  from  the  particulars,  the  particulars  have 
the  attributes  summarised  in  the  definition  ;  and,  therefore  they 
have  whatever  can  be  shown  to  follow  from  those  attributes 
But  It  frequently  happens  that  the  argument  rests  partly  on  the 
qualities  connoted  by  the  class  name  and  partly  on  many  other 
tacts. 

In  Geometry,   the  proof  of  a  theorem  depends  not  only  upon  the 
definnton  of  the  figure  or  figures  directly  concerned,  but  also  uLn  one 
or  more  axioms  and  upon  propria  or  constructions  already  established 
Thus^  m   Euclid's   Fifth    Proposition,    the   proof  that    L   angles  a. 
he    base  of    an   isosceles   triangle  are   equal,   depends  not   on]      on 
the  equality  of  the  opposite  sides,  but  upon  this  together  with  the  con 
strucuon  that  shows  how  from  .he  greater  of  two  lines  a  part  may  be  cut 
off  equal  to  the  less,  the  proof  (or  assumption)  that  triangles  that  can  bl 
concen-ed  to  coincide  are  equal,  and  the  a..iom  that  if  equals  be  Taken 
from   equals    the   remainders   are    equal.      Similarly,    in    Biology  Tf 
colourmg    favourable   to   concealment   is  a  proprium  of    carnivorous 
animals,   .t  .s  not  deducible   merely  from    their  predatory   characte 
or  any  other  attribute  entering  into  the  definition  of  any    spedes  I 
them,    but   from  their  predatory  character   together  with  the  cause 
summarised  ,n  the  phrase  ■  Natural  Selection';  that  is.  competition  fo   a 
livelihood,   and    the  destruction  of  those  that  labour  under  anv  d  s 


298      LOGIC:    DEDUCTIVE   AND   INDUCTIVE 


advantages,  of  which  conspicuous  colouring  would  be  one.  The  par- 
ticular colouration  of  any  given  species,  again,  can  only  be  deduced  by 
further  considering  its  habitat  (desert,  jungle  or  snow-field)  :  a  circum- 
stance lying  wholly  outside  the  definition  of  the  species. 

The  validity  of  an  argument  based  partly  or  wholly  on  a 
Definition  depends,  in  the  first  place,  on  the  existence  of 
things  corresponding  with  the  Definition — that  is,  having  the 
properties  connoted  by  the  name  defined.  If  there  are  no 
such  things  as  isosceles  triangles,  Euclid's  Fifth  Proposition  is 
only  formally  true,  like  a  theorem  concerning  the  fourth 
dimension  of  space  :  merely  consistent  with  his  other  assump- 
tions. But  if  there  are  any  triangles  only  approximately 
isosceles,  the  proof  applies  to  them,  making  allowance  for  their 
concrete  imperfection  :  the  nearer  their  sides  approach  straight- 
ness  and  equality  the  more  nearly  equal  will  the  opposite 
angles  be. 

Again,  as  to  the  existence  of  things  corresponding  with  terms  defined. 
Dr.  Venn  has  pointed  out  that  '  existence  '  may  be  understood  in  several 
senses  :  (i)  merely  for  the  Reason,  like  the  pure  genera  and  species  of 
Porphyry's  tree  ;  the  sole  condition  of  whose  being  is  logical  consis- 
tency: or  (2)  for  the  Imagination,  like  the  giants  and  magicians  of 
romance,  the  heroes  of  tragedy  and  the  fairies  of  popular  superstition, 
whose  properties  may  be  discussed  and  verified  by  appeal  to  the  right 
documents  and  authorities  (poems  and  ballads)  :  or  (3)  for  Perception, 
like  plants,  animals,  stones  and  stars.  We  may  argue,  therefore,  from 
the  definition  of  a  fairy,  or  a  demigod,  or  a  dragon,  and  deduce  various 
consequences  without  absurdity,  if  we  are  content  with  poetic  consis- 
tency and  the  authority  of  myths  and  romances  as  the  test  of 
truth. 

When,  however,  we  pass  into  the  region  of  concrete  objects, 

whose  properties  are  causes,  and  not  merely  determinations  of 

space  (as  in  Geometry),  we  meet  with  another  condition  of  the 

validity  of  any  argument   depending  on  a  Definition  :  there 

must  not  only  be  objects  corresponding  to  the  definition  ;  but 

there  must  be  no  other  causes  counteracting  those  qualities  on 

whose  agency  our  argument  relies.      Thus,  though  we  may 

infer  from  the  quality  of  co-operation  connoted  by  civilisation, 

that  a  civilised  country  will  be  a  wealthy  one,  this  may  not  be 

found  true  of  such  a  country  recently  devastated  by  war  or 


DEFINITION   OF  COMMON   TERMS  299 

other  calamity.  Nor  can  co-operation  always  triumph  over 
d  sadvantageous  circumstances.  Scandinavia  is  so  poor  in  the 
g.fe  of  nature  that  are  favourable  to  industry,  that  it  is  not 
wealthy  ,„  spUe  of  civilisation  :  still,  it  is  far  wealthier  than  i 
would  be  m  the  hands  of  a  barbarous  people.  In  short,  while 
argumg  from  a  Definition,  we  can  only  infer  the  teJe.cy  of 

ZCr      '^'T'''"''"'   '""'"'^^^    '■"   "  ■'    *e    unqualified 
reahsafon  of  such  a  tendency  must  depend  upon  the  Absence 

of  counteracting  causes.     As  soon  as  we  leave  the  region  of 

pure  conceptions  and  make  any  attempt  to  bring  our  specula- 

tions  hometo  the  actual  phenomena  of  nature  or  of  human 

ibligltLn       "'°"  "'"■"^'  "'"""^  '^'^•=°"*^^^"  ""--«-g 


CHAPTER  XXIV 


FALLACIES 


§  I.  A  Fallacy  is  any  failure  to  fulfil  the  conditions  of 
Proof.  If  we  neglect  or  mistake  the  conditions  of  proof 
unintentionally,  whether  in  our  private  meditations  or  in 
addressing  others,  it  is  a  Paralogism  :  but  if  we  endeavour 
to  pass  off  upon  others  evidence  or  argument  which  we  know 
or  suspect  to  be  unsound,  it  is  a  Sophism. 

Fallacies,  whether  paralogisms  or  sophisms,  may  be  divided 
into  two  classes :  (a)  the  Formal,  or  those  that  can  be  shown 
to  conflict  with  one  or  more  of  the  truths  of  Logic,  whether 
Deductive  or  Inductive  ;  as  if  we  attempt  to  prove  an  universal 
affirmative  in  the  Third  Figure  ;  or  to  argue  that,  as  the  average 
expectation  of  life  for  males  at  the  age  of  20  is  39J  years, 
therefore  Alcibiades,  being  20  years  of  age,  will  die  when  he 
is  39i;  (^0  the  Material,  or  those  that  cannot  be  clearly 
exhibked  as  transgressions  of  any  logical  principle,  but  are 
due  to  hasty  or  superficial  inquiry  or  confused  reasonmg ; 
as  in  adopting  premises  on  insufficient  authority,  or  without 
examining  the  facts ;  or  in  mistaking  the  point  to  be  proved. 

§  2.  Formal  Fallacies  of  Deduction  and  Induction  are, 
a\\  of  them,  breaches  of  the  rule  '  not  to  go  beyond  the 
evidence.'  As  a  detailed  account  of  them  would  be  little 
else  than  a  repetition  of  most  of  the  foregoing  chapters,  it 
may  suffice  to  recall  some  of  the  places  at  which  it  is  easiest 
to  go  astray. 

(I)  It  is  not  uncommon  to  mistake  the  Contrary  for  the  Contradictory, 
^s— A  is  not  taller  than  B,    .'.  he  is  shorter. 


FALLACIES 


301 


(2)  To  convert  ^.  or  O.  simply,  as- 

All  Money  is  Wealth   .-.   All  Wealth  is  Money, 
or-Some  Wealth  is  not  Money   .-.    Some  Money  is  not  Wealth. 
In  both  these  cases.  Wealth,  though  undistributed  in  the  convertend. 
IS  distributed  in  the  converse. 

(3)  To  attempt  to  syllogise  with  two  premises  containing  four  terms,  as 

The  Papuans  are  savages  ; 
The  Javanese  are  neighbours  of  the  Papuans  : 
.-.  The  Javanese  are  savages. 
Such  an  argument  is  excluded  by  the  definition  of  a  Syllogism,  and 
presents  no  formal  evidence  whatever.     We  should  naturally  assume 
that  any  man  who  advanced  it  merely  meant  to  raise  some  probability 
that   '  neighbourhood  is  a  sign  of  community  of  ideas  and  customs  ' 
But.  if  so,  he  should  have  been  more  explicit.     There  would,  of  course, 
be  the  same  failure  of  connection,  if  a  fourth  term  were  introduced  in 
the  conclusion,  instead  of  in  the  premises. 

(4)  To  distribute  in  the  conclusion  a  term  that  was  undistributed  in 
the  premises  (an  error  essentially  the  same  as  (2)  above),  i.e..  Illicit 
process  of  the  major  or  minor  term,  as— 

Every  rational  agent  is  accountable ; 
Brutes  are  not  rational  agents : 
.-.    Brutes  are  not  accountable. 
In  this  example   (from  Whately),  an  illegitimate  mood  of  Fig.  I     the 
major  term,  '  accountable/  has  suffered  the  illicit  process ;  since,  in  the 
premise,  it  is  predicate  of  an  affirmative  proposition  and,   therefore 
undistributed;  but,  in  the  conclusion,  of  a  negative  proposition  and' 
therefore,  distributed.     The  fact  that  nearly  everybody  would  accept 
the  conclusion  as   true,   of  course,  might  lead   them   to  overlook   the 
inconclusiveness  of  the  formal  proof. 
Again,  All  men  are  two-handed  ; 

All  two-handed  animals  are  cooking  animals  : 
.-.   All  cooking  animals  are  men. 
Here  we  have  Bramantip  concluding  in  A. ;  and  there  is,  formally 
an  illicit  process  of  the  minor  ;  though  the  conclusion  is  true  ;  and  the 
evidence,  such  as  it  is,  is  materially  adequate.    (Of  course,  '  two-handed.' 
being  a  peculiar  Differentia,  is  nugatory  as  a  middle  term,  and  may  be 
cut  out  of  both  premises  ;  but  '  cooking  '  is  a  Proprium  peculiar  to^he 
species  Man;  so  that  these  terms  might  be  related  in  U.,All  men  aye 
all  cookers;  whence,  by  conversion,  All  cookers  are  men.) 

(5)  To  omit  to  distribute  the  middle  term  in  one  or  the  other  premise 
as — 

All  verbal  propositions  are  self-evident ; 
All  axioms  are  self-evident : 
.'.   All  axioms  are  verbal  propositions. 
This  is  an  illegitimate  mood  in  Fig.  II. ;  in  which,  to  give  any  con- 


3o: 


LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


elusion,  one  premise  must  be  negative.  It  may  serve  as  a  formal 
illustration  of  Undistributed  Middle;  though,  as  both  premises  are 
verbal  propositions,  it  is  materially  not  syllogistic  at  all,  but  an  error  of 
classification  ;  a  confounding  of  co-ordinate  species  by  assuming  their 
identity  because  they  have  the  generic  attribute  in  common. 

(6)  To  simply  convert  a  hypothetical  proposition,  as  — 

If  trade  is  free,  it  prospers ; 
.-.    If  trade  prospers,  it  is  free. 

Clearly,  this  is  similar  to  the  simple  conversion  of  the  categorical  A.  ; 
since  it  takes  for  granted  that  the  antecedent  is  co-extensive  with  the 
consequent,  or  (in  other  words)  that  the  freedom  of  trade  is  the  sole 
condition  of,  or  (at  least)  inseparable  from,  its  prosperity. 

The  same  assumption  is  made  if,  in  a  hypothetical  syllogism,  we  try 
to  ground  an  inference  on  the  affirmation  of  the  consequent  or  denial  of 

the  antecedent,  as — 

If  trade  is  free,  it  prospers: 
It  does  prosper ; 
.'.   It  is  free. 

It  is  not  free  ; 
.-.    It  does  not  prosper. 
Neither  of  these  arguments  is  formally  good  :  nor,  of  course,  is  either 
of  them  materially  valid,  if  it  be  possible  for  trade  to  prosper  in  spite  of 
protective  tariffs. 

An  important  example  of  this  fallacy  is  the  prevalent  notion,  that  if 
the  conclusion  of  an  argument  is  true  the  premises  must  be  all  right ; 
or,  that  if  the  premises  are  false  the  conclusion  must  be  erroneous. 

For,  plainly,  that  — 

If  the  premises  are  true,  the  conclusion  is  true, 
is  a  hypothetical  proposition  ;  and  we  argue  justly— 

The  premises  are  true ; 
.'.   The  conclusion  is  true  ; 
or.  The  conclusion  is  false  ; 
.-.   The  premises  are  false. 
This  is  valid  for  every  argument   that  is  formally  correct ;  but  that 
we  cannot  trust  the  premises  on   the  strength  of  the  conclusion,  nor 
reject  the  conclusion  because  the  premises  are  absurd,  the  following 

example  will  show  : 

All  who  square  the  circle  are  great  mathematicians ; 
Newton  squared  the  circle: 
.-.    Newton  was  a  great  mathematician. 
Here  our  conclusion  is,  no  doubt,  true ;  but  the  premises  are  intoler- 
able.    If.  then,  to-day  the  inferences  of  our  favourite  orator  are  very 
much  to'  our  taste,   we  had  better  not  for  that  reason  embrace  his 
premises   without   examining   them.     Another   day,    in  circumstances 
slightly  different,  they  may  have  other,  less  innocent  results. 


FALLACIES 


3^3 


How  the  taking  of  Contraries  for   Contradictories  may  vitiate  Dis- 

ih:ri^'Srer"'  "^^^-^-^^^ '- '-  -^^^-^^y^^^^n^^^ 

§  3.  Formal  Fallacies  of  Induction  consist  in  supposing 
or  inferring  Causation  without  attempting  to  prove  it  or  in 
pretending  to  prove  it  without  satisfying  the  Canons  of 
observation  and  experiment  :  as— 

as^'.l^whvT  ^^^f""^^^^  ->'^hing  that  is  not  a  concrete  event: 

Z    reZJ'    7  T       '^"  '^"'^  °"^y  ^"  °"^  P^^^^-     ^"^^  should  give 
he    reason    .  for  this  expression  includes,  besides  evidence  of  causation 
the  principles  of  formal  deduction,  logical  and  mathematical 

(2)  To  argue,  as  if  on  Inductive  grounds,  concerning  the  cause  of 
the  Universe  as  a  whole.    This  may  be  called  the  fallacy  of  transcenden 
inference .  since  the  Canons  are  only  applicable  to  instances  of  evem 

uniiuT       ""''"'  '  '"''  ''""^^  ^'^'  ''''''  ^^^^  ^^h-h  ^^  -  it^  n~ 

(3)  To  mistake  co-existent  phenomena  for  cause  and  effect  •  as  when  a 
man.  wearing  an  amulet  and  escaping  shipwreck,  regards  the  amulefas 
the  cause  of  his  escape.  To  prove  his  point,  he  must  either  get  aga" 
into  exactly  the  same  circumstances  without  his  amulet,  and  then  be 
drovvned  -according  to  the  method  of  Difference  ;  or,  shi  king  the  onl 

TITJ  T  '"'.'"""^^  "P  "^^'  "^^^^  ^^^^~^-  h^  n-^t  show 
(a)  that  all  who  are  shipwrecked  and  escape  wear  amulets,  and  (b)  thai 
their  cases  agree  in  nothing  else;  and  (.).  by  the  Joint  Method     ha    al 
who  are  shipwrecked  without  amulets  are  drowned.     And  ev;n  if  ht 
evidence,  according   to   Agreement,   seemed   satisfactory  in   a,I    these 
points.  It  would  still  be  fallacious  to  trust  to  it  as  proof  of  direc   causa 

Tthir  •:  Ts^'r  V""  ^'"  "^^^.^^^  ^^^^--^^  ^^  never  Tuf^:-::; 

tor  this  ^  It  IS  only  by  experiment  in  prepared  circumstances  that  we 
can  confidently  trace  sequence  and  the  transfer  of  energy 

dpLnT  ;'  '^^  '^'^^""^  ^''°'  °^  "^i^'^king  causal  connection  for  in- 
dependent co-existence :  as  if  anyone  regards  it  as  merely  a  curious 
coincidence  that  great  rivers  generally  flow  past  great  towns      In  thi 
case,  however,   the  evidence  of    connection  does  not  depend  me  eW 
upon  direct  Induction.  ^         merely 

(4)  Post  hoc   ergo  propter  hoc:  to  accept  the  mere  sequence  of  pheno- 

caTse  :r  T?""  °'^^^  "P^^^^'-  ^^  P^^^'^"^  ^^^^  ^h'  phenomena  Le 
cause  and  effect,  or  connected  by  causation.     This  is  a  very  natural 

error:  for  although,  the  antecedents  of  a  phenomenon  being  nume  ous 

mos   of  them  cannot  be  the  cause,  yet  it  is  among  them  that  the  cause 

must  be  sought.     Indeed,  if  there  is  neither  time  nor  opportunity  for 

analysis,  it  may  seem  better  to  accept  any  antecedent  as  a  cause  (or  at 

■least,  as  a  sign)  of  an  important  event  than  to  go  without  any  guide 


/ 


.^^ 


304      LOGIC:    DEDUCTIVE    AND   INDUCTIVE 

And.  accordingly,  the  vast  and  complicated  learning  of  omens,  augury, 
horoscopy  and  prophetic  dreams,  relies  upon  this  maxim  ;  for  whatever 
the  origin  of  such  superstitions,  a  single  coincidence  in  their  favour  trium- 
phantlv  confirms  them.  It  is  the  besetting  delusion  of  everybody  who 
has  wishes  or  prejudices,  that  is.  of  all  of  us  at  some  time  or  other; 
for  then  we  are  ready  to  believe  without  evidence.  And.  plainly,  the 
fallacy  consists  in  judging  off-hand,  without  any  attempt,  either  by 
deductive  or  inductive  methods,  to  eliminate  the  irrelevant  ante- 
cedents;   which,   however,    may   include   all     the   most   striking    and 

specious.  .     V 

(5)  To  regard  the  Joint-Effects  (whether  simultaneous  or  successive) 
of  a  common  cause  as  standing  in  the   direct  relation  of  cause   and 
effect      Probablv  no  one  supposes  that  the  falling  of  the  mercury  in  his 
thermometer  is  the  cause  of  the  neighbouring  lakes  freezing.     True,  it 
is  the  antecedent,  and  (within  a  narrow  range  of  experience)  may  be 
the  invariable  antecedent  of  the  frost;  but.  besides  that  the  two  events 
are  so  unequal,  everv  one  is  aware  that  there  is  another  antecedent,  the 
fall  of  temperature,  which  causes  both.     Yet  in  many  cases,  the  same 
kind  of  mistake  is  made  from  not  remembering  that,  to  justify  indue- 
tively  our  belief  in  a  cause,   the  instances  compared  must  agree,  or 
differ,  in  one  circumstance  only  (besides  the  effect).     The  flowmg  tide 
is  an  antecedent  of  the  ebbing  tide  ;  it  is  invariably  so.  and  is  equal  to 
it  •  but  it  is  not  the  cause  of  it :  other  circumstances  are  present ;  and 
the  moon,  chieflv,  is  the  cause  of  both  flow  and  ebb.     In  several  in- 
stances, States  that  have  grown  outrageously  luxurious  have  declined  in 
power     that  luxury  caused  the  downfall  may  seem  obvious,  and  capable 
of  furnishing  a  moral  lesson  to  the  young.     Hence   other  important 
circumstances  are  overlooked,  such  as  the  institution  of  slavery,  the 
corruption  and  rapacity  of  officials  and  tax-gatherers,  an  army  too  power- 
ful for  discipline  ;  any  or  all  of  which  may  be  present,  and  sufficient 
to  explain  both  the  luxury  and  the  ruin. 

(6)  To  mistake  one  condition  of  a  phenomenon  for  the  whole  cause. 
To  speak  of  an  indispensable  condition  of  any  phenomenon  as  the  cause 
of  it   may  be  a  mere  conventional  abbreviation ;  and  in  this  way  such  a 
mode  of  expression  is  common  not  only  in  popular  but  also  in  scientific 
discussion.     Thus  we  say  that  a  temperature  of  33°  F  ^^  ^  cause  ot 
the  melting  of  ice;  although  that  ice  melts  at   33    F.   ^^^\  ^^''^^' 
depend  upon  something  in  the  nature  of  water ;  for  every  solid  has  its 
ow^  melting-point.     As  long.  then,  as  we  remember  that;  cause,   used 
in  this  sense,  is  only  a  convenient  abbreviation,  no  harm  is  done  ;  but. 
if  we  forget  it.  fallacy  may  result ;  as  when  a  man  says  that  the  cause 
of  a  financial  crisis  was  the  raising  of  the  rate  of  discount,  neglecting 
the  other  conditions  of  the  market ;  whereas,  in  some  circumstances  a 
rise  of  the  Bank-rate  may  increase  public  confidence  and  prevent  a 
crisis. 


FALLACIES 


305 

cause  or  an  indispensabL  condition  of  ?J  u  ^  '"■*"'"  ^"'e-«!ent  is  a 
tion.  If,  ..erefoL,  it  is^  rpr:„rl'aT— :  '"'^-'"-''«- 
either  experiment  directly  uoon  th^  r.th         "'^.'*°'^  '^ause,  we  must 

Method  of  Residues  and 'd  d^ctit  reto^ni^r'"""^'  "  ^^'°^'  '°  *^ 
without   showing,   where   such  Zt.?  ^'  """^  """«•«  be  content 

cause  and  the  gi:;„phen^rn'n~u"a;^  •"^^""^'  ''"  "^«  ^"^»-'' 

eff2t,TratX:ntit%Trrrnno°'  '  ''^  -"-  ^^  ">«  -"o'e 
mistakes  of  private  conduct  and  of  leZZTrT     ""'''''  =^"  ""^ 

temporary  lassitude  by  a  stimuIan^a„Tst^an::.h:^•'^  '' ^  ^°  ^"" 
lish  a  new  industry  by  protective  dnl         IT         ''™'' ■  '°  ^^'^b- 

rest  of  the  country';  to  gag  the  press  and"  '''^■•^''>'J-P°-rish  the 
into  conspiracy  ;  to  build  ^nalm^  house  and"  th""^  "'  ^i^-'-'ed 
into  the  parish,  raise  the  rates  ar^H  H^  '^"'^''^  *'^='<^'  P^^Pe" 

/»i  x„  J  J  '  ^""  discourage  industrv 

(8)  To  demand  greater  exactness  in  the  estimate  n> 
than  a  given  subject  admits  of     In  ,h         ^"™^'«  °f  causes  or  effects 

Sociology,  PsycLlogy,Tis°tften  ^ZZlZt^  ^T '  '''°'°^^' 
the  conditions  of  a  given  phenomenon^a  fbeln  ^1  ""f '"'  *"'  "" 
Its  consequences  have  been  traced.  The  causes  of  th"'  "'  *"'  "" 
Revolution  have  been  carefully  investigated  and  still'  ^""^^  ^I'"* 
whether  they  have  all  been  discovered  or  whether  h  -"^  ™^^  '^""'^ 
importance   has  been  rightly  determTneH     K  !  ^"'  =°'"Pa'-ative 

reasonable  to  treat  that  even,  °^'^™'"^'^ '  t""'  "  would  be  very  un- 
totle  observes  n  h  s  s'lv  hL  a  oT'T"','"'  ""-'^"'gible.  'Aris- 
degree  of  precision  is  o  be  exoec  ed  '  T^''^  """'^  '"'°-^  ""at 
trovertists,  being  sufficient  duca  fd  TndTat  "TT  ■  "^"^^'  ~"- 
do  not  comment  superciliously  upo'  the  IT  '  'r""^  ^"^  P'^^' 
demonstration  where  it  is  of  course  roUaL^r^  °'  mathematical 

Jse  rrt^rrenr^fTm'iter"" '"  "-^  ^^  ^"  --""'«-" 

tions  of  forces  and,  tre  efo'rfor  m  H^fi"''^"'''""''^  ^°^  "^"  <^°'"''i"^- 
although  we  often  sayThrNaLr'f  p ""^  °'  "'^  ^^f-''  Thus, 
cause  of  his  downfall  ve    the  effe.  u-'"^"  expedition  was  the 

conditions.  Had  ^^'Il^sVoT^lZru^^::  TadT ^""^  '"*- 
exceptionally  mild,  had  the  Prussians  InH  a     .:  *^  """'^''  ^^^ 

him,  the  eve'nt  might  have  bfen  y";  d^fferett  uTs  "V^  ^^^'"^' 
liberties  of  modern  Europe  to  the  Iv.„r  f  ./  J^*  '°  *''^<=«  '^e 
powers  of  perception  are  so  uneq  al  .o  thtsutl^tro^",  '"'r^'  °" 
m  experimental  science  there  is  time  iT  >  T  "^""■^'  "'*'  ^^n 
between  what  we  treat  as  a  cause  and  tLe  el  r"'"  "'''"'''  '°  °'=^" 
such  cases  the  -ictly  unconai.i:n:"lt  S^brrctli^^     '" 

(10)  To  neglect  the  negative  conditions  to  which  a  cau^.r  t 
When  we  say  that  water  boils  at  .xa»  F.,  we  meaf..  prrd^'thrpC 

u 


> 


3o6     LOGIC  :   DEDUCTIVE   AND   INDUCTIVE 

s„.e  be  not  greater  that,  that  of  the  ^--^X^:XX:;^^^e 

for  under  a  greater  P^««="^f  J'^'^^  ™'"  "°  temperature.  Irt  the  usual 
whilst  under  less  pressure  .tbo.ls  ^'  ^  1°-^^^;'^P^3  ,,„ed  •  disturbing,' 
statement  of  a  la«  of  causation,  what  are  somet.m  ^^^ 

frustrating.'  ■counteracting'  --—■=;'■  .f.f;  ;.ement  of  such 
—  ^^a^m^t^^ro^^    ;^^^^^^^^ 

favourable,  or  in  the  absence  of  contrary  forces.  ^^.^  ^^  ^^^^^ 

,„)  It  is  needless  to  repeat  "^'-^'^^^^f^^^'^^eglect  of  a  possible 
fallacies  that  beset  -ducfve  proof ,  su  h  as^;;^^,  »,^  ^„„,,i,,d ;  the 
plurality  of  causes  where  the  ^""^^  the  chief  errors  to 

extension  of  empirical  laws  beyond  adjacent  cases  ^  application  of 

.hich  the  estimate  of  analogies  -"^  P  "^^'^The  r  liance'^upon  direct 
the  principles  of  classification  are  hab  e^  and  th  ^^^^^^^  ^^  ^^^^ 
Induction   where   the   aid  of  deduction   may  ^^^^^^.^^ 

observation  «>^ere  experiment  m^^^^^  .T^ls  on°«>-'  -"'°^'  '*^'= 
that  may  be  avoided  b>  aanerin^ 

"1  'f  There   remain    many  ways   in   which   arguments  fall 
9  4-    inere    icn.  j  thouah  they  cannot 

short  of  a  tolerable  standard  of  proof,  thougn        y 

i„  'h.™.n,isJ!  o,  i.  .h.  conclu.i.n,  o,  ,„  .b.  a„empt  .0 
connea  a  conclu.ion  .i*  -h.  P«-  ^|,,^, 

rT^   Now  the  premises  of  a  souna  argumc 
J    lid  deductions,  or  valid  inductions,  or  J^"-^-;^;-  ^ 
^r   nxioms      In   an   unsound   argument,   then,   wtiose 
uons    or   ^''•o'"  ;^    /"  ^^^^^   deduction   or   induction, 

re:^L::Vayr      uce'd  to  logical  rules;  and  its  fa.lure 
f  the  eore  a     ogical  fallacy'  such  as  we  have  already  dis- 
cussed     U  follow:  that  an  extra-logical  fallacy  of  the  prem.se 
must  lie  in  what  cannot  be  reduced  to  rules  of  evidence,  that 

is,  bad  observations  or  f2rZ"c.n  only  be  fallacious   if 
(2)   As  to  the   conclusion,  this  can  umy 


/ 


FALLACIES  3^^ 

!r!  T'"  /=°"''"^'°"  has  been  substituted  for  that  which 
was  to  have  been  proved. 

(3)  Fallacies  in  the  connection  between  premises  and 
conchision,  if  all  the  propositions  are  distinctly  and  explicitly 
stated,  become  manifest  upon  applying  the  rules  of  Logic. 
Fallacies,  therefore,  which  are  not  thus  manifest,  and  so 
are  extra-logical,  must  depend  upon  some  sort  of  slurring 
confusion,  or  ambiguity  of  thought  or  speech 

/A  .l  ^"'Tff  ^''"'''''  °^  Observation,  Mill  distinguishes 
(r)  those  of  Non-observation,  where  either  instances  of  the 
presence  or  absence  of  the  phenomenon  under  investigation 
or  else  some  of  the  circumstances  constituting  it  or  attending 
upon  >t,  though  important  to  the  induction,  are  overlooked 
These  errors  are  implied  in  the  Formal  Fallacies  of  Induction 
already  treated  of  in  §  3  (paragraphs  (3)  to  (7)). 

Mill's  class  (2)  comprises  fallacies  of  Malobservation  Mal- 
observation  may  be  due  to  obtuseness  or  slowness  of  percep- 
tion;  and  It  IS  one  advantage  of  the  physical  sciences  as  means 
of  education,  that  the  training  involved  in  studying  them  tends 
to  cure  these  defects. 

But  the  occasion  of  error  upon  which   Mill  most  insists 
.s  our  proneness  to  substitute   a   hasty   inference   for  a  iust 
representation  of  the  fact  before  us;  as  when  a  yachtsman, 
all   agog   for   marvels,    sees   a   line   of   porpoises    and   takes 
them   for   the   sea-serpent.     Every  one   knovvs  what  it  is  to 
mistake  a  stranger  for   a   friend,  a  leaf  for  a  sparrow,  one 
word   for   another   (X   persisted    in    reading   Unsertesen    as 
untersetzen).     The  wonder  is  that  we  are  not  oftener  wrong  • 
considering  how  small  a  part  present  sensation  has  in  percen' 
tion,  and  how  much  of  every  object  observed  is  supplied  by  a 
sort  of  automatic  judgment.     You  see  something  brown,  which 
your  perceptive  mechanism  classes  with  the  appearance  of  a 
cow  at  such  a  distance;  and  instantly  all  the  other  properties 
of  a  cow  are  supplied  from  the  resources  of  former  experience  • 
but  on  getting  nearer,  it  turns  out  to  be  a  log  of  wood      It  is 
some  protection  against  such   errors   to   know  that   we  are 


laiMMBliaiaMMIifliHIil 


3o8      LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

subject  to  them  ;  and  the  Logician  fulfils  his  duty  in  warning 
us  accordingly.  But  the  matter  belongs  essentially  to  Psy- 
chology ;  and  whoever  wishes  to  pursue  it  will  find  a  thorough 
explanation  in  Prof.  Sully's  volume  on  Illusions. 

Another  error  is  the  accumulation  of  useless,  irrelevant 
observations,  from  which  no  proof  of  the  point  at  issue  can  be 
derived.  It  has  been  said  that  an  important  part  of  an  induc- 
tive inquirer's  equipment  consists  in  knowing  what  to  observe. 
The  study  of  any  science  doubtless  educates  this  power  by 
showing  us  what  observations  have  been  effective  in  smiilar 
cases  :  but  something  depends  upon  genius.  Observation  is 
generally  guided  by  hypotheses  :  he  makes  the  right  observa- 
tions who  can  frame  the  right  hypotheses  ;  whilst  another  over- 
looks things,  or  sees  them  all  awry,  because  he  is  confused  and 
perverted  by  wishes,  prejudices  or  other  false  preconceptions  ; 
and  still  another  gropes  about  blindly,  noting  this  and  docket- 
ing that  to  no  purpose,  because  he  has  no  hypothesis,  or  one 
so  vague  and  ill  conceived  that  it  sheds  no  light  upon  his 

path. 

§  6.  The  second  kind  of  extra-logical  Fallacy  lying  in  the 
premises,  consists  in  offering  as  evidence  some  verbal  jingle 
or  assertion  which  is  entirely  baseless  :  it  is  generally  known  as 
petitio  prhicipii,  or  begging  the  question.  The  question  may 
be  begged  in  three  ways:— (i)  there  are  what  Mill  calls 
Fallacies  a  priori,  mere  assertions,  pretending  to  be  self- 
evident,  and  often  sincerely  accepted  as  such  by  the  author 
and  some  infatuated  disciples,  but  in  which  the  cold-blooded 
spectator  sees  either  no  sense  at  all,  or  palpable  falsity. 

These  sham  axioms  are  (grievous  to  confess)  not  uncommon  in  the 
writings  of  the  greatest  philosophers.  There  are  thousands  of  them ; 
and  probably  every  one  is  familiar  with  the  following  examples  :  That 
circular  motion  is  the  most  perfect;  That  every  body  strives  toward  its 
natural  place  ;  That  like  cures  like  ;  That  every  bane  has  its  antidote; 
That  the  soul  is  especially  active  and  intelligent  in  dreams;  That 
pleasure  is  nothing  but  relief  from  pain  ;  That  the  good,  the  beautiful 
and  the  true  are  inseparable;  That,  in  trade,  whatever  is  somewhere 
gained  is  somewhere  lost;  That  only  in  agriculture  does  nature 
assist  man  ;  That  a  man  may  do  what  he  will  with  his  own  ;  That  some 


FALLACIES  309 

men  are  naturally  born  to  rule  and  others  to  obey.  Now  some  of  these 
doctrines  are  specious  enough ;  whilst  as  to  others,  how  they  could  ever 
nave  been  entertained  arouses  a  wonder  that  can  only  be  allayed  by  a 
lengthy  historical  and  psychological  disquisition. 

(2)  Verbal  propositions  offered  as  proof  of  some  matter  of 
fact. 

These  have,  indeed,  one  attribute  of  Axioms:  they  are  self-evident  to 
any  one  who  knows  the  language  ;  but  as  they  only  dissect  the  meaning 
of  words,  nothing  but  the  meaning  of  words  can  be  inferred  from  them 
If  anything   further   is   arrived   at,    it   must   be   by  the  help  of  real 
propositions.      How  common  is  such  an  argument  as  this:    'Lying 
IS  wrong,  because  it  is  vicious '-the  implied  major  premise  being  that 
•  what  IS  vicious  is  wrong.'     Now  if  anybody  hesitates  whether  to  be  a 
liar  or  not.  good  reasons  can  be  given  him  for  abstaining  ;  but  the  above 
argument  only  shows  that  lying  is  called  wrong  ;  and  this  the  impending 
liar  already  knew.     The  argument,  therefore,  must  be  supplemented  by 
a   further  premise,    that    'what   is   called   wrong  in  English  is  most 
probably  something  that  ought  to  be  avoided ' :    but    this    is    a    real 
proposition,  which  to  a  foreigner  might  seem  to  need  a  vast  amount  of 
evidence.     So  let  us  hope  there  is  some  shorter  and  more  cosmopolitan 
way  of  restraining  the  moral  plunger.     Still,  such  arguments,  though 
bad  Logic,  often  have  a  rhetorical  force :  to  call  lying  not  only  wrong 
but  vicious,  may  be  dissuasive  by  accumulating  associations  of  shame 
and  Ignominy. 

Definitions,  being  the  most  important  of  verbal  propositions  (since 
they  imply  the  possibility  of  as  many  other  verbal  propositions  as  there 
are  defining  attributes  and  combinations  of  them),  need  to  be  watched 
with  especial  care.  If  two  disputants  define  the  same  word  in  different 
ways,  with  each  of  the  different  attributes  included  in  their  several 
definitions  they  may  bring  in  a  fresh  set  of  real  propositions  as  to  the 
agency  or  normal  connection  of  that  attribute.  Hence  their  conclusions 
about  the  things  denoted  by  the  word  defined,  diverge  in  all  directions 
and  to  any  extent.  And  it  is  generally  felt  that  a  man  who  is  allowed 
o  define  his  terms  as  he  pleases,  may  prove  anything  to  those  who 
through  ignorance  or  inadvertence,  grant  that  the  things  that  those 
terms  stand  for  have  the  attributes  that  figure  in  his  definitions. 

(3)  Circulus  in  demonstrando,  the  pretence  of  giving  a  reason 
for  an  assertion,  whilst  in  fact  only  repeating  the  assertion 
itself— generally  in  other  words. 

In  such  cases  the  original  proposition  is,  perhaps,  really  regarded  as 
self-evident,  but  by  force  of  habit  a  man  says  '  because ' ;  and  then  after 
vainly  fumbling  in  his  empty  pocket  for  the  coin  of  reason,  the  same 


3,0      LOGIC:   DEDUCTIVE  AND   INDUCTIVE 

■  Hve.,  event  ^-^TZ:s^^:^^^^  P^e-e.stL; 
nomena.  and  this  implies  a  u^"^  ,  •     operation 

which  can  only  have  ^enpo.:b...the^-^^^^^^^^^^^    ^^  ^^P^_^^_ 

capable  of  transforming  .t       O^' ^g^m  .  ^j^^^^id  not  imply 

because  it  is  urong  to  shed  blood.      But,  plainly  ^^^^ 

bloodshed,  the  unlawfulness  of  this  could  be  notfung  ^^amst 

more  serious  any   matter  is,   *«  --^'XiteKe   s^h  wholesome 
to  reason  thoroughly  about  it,  or  to  content  ""^sehes 
assertions.     How  many  •  arguments  '  are  superfluou! 

§,  The  Fallacy  of  surreptitious  conclusion  (/.§-«<^r<z<. 
elelki),  the  mistaking  or  obscuring  of  the  proposition  really 
at  issue,  whilst  proving  something  else  instead. 

This  may  be  done  by  substituting  ^  P-tif  t^^wToTact' th^e 
universal,  or  an  universal  for  a  particular.     Thus,  ne  wn 
^rTc^i^e  of  giving  in  charity  must  not  be  -te^t  to^how  that  .t^^as,  in 
Ls  or  ,^at  case,  degreed  ^^-ec^rnolt^frr gUing  alms  in  a 
ceptionally  weak     Or,  again,  '°  ^'^^"^^  ^      ^  ,^x  tendency 

particular  case,  it  is  not  enough  to  show  that  tne  g  j^^dency 

of  almsgiving  is  injurious ;  for,  by  taking  pains,  the  general  y 

■"  sUerrm^  ratumtt  establishing  a  wholly  irrelevant  conclusion  is 
subX:^  for  ..\,u.,u,.u.,.  a  ran.   ^^^^^^l^]^^ 
aoolo-ists  for  Charles  I.,  who  try  to  defend  him  as  a  kin„   D>      g 
?w  he  was  a  good  judge  of  paintings  and  indulgent  to  his  wife. 
'   To    h^.    4s^  Falfacies'belongs  the  arg.nnen,.,,.  a.i  '-""«""■  J*;-^^^ 
insists  In  showing  not  that  a  certain  proposition  is  true,  but  that 
cX  ought  to  accept  it  in  consistency  with  his  Cher  opinions^  Thu  . 
l"""ry  parish  the  cost  of  education  ought  to  be  paid  out  °"^eja^^- 
ImLsI  have  said  that  there  can  be  no  sound  economy,  unless  local 
you,  atleast,  navesaici  iiiau  I  R„t  whether  this  is  a  fallacy 

expenses  are  defrayed  from  local  funds.      But  whe  her  tni  y 

fnconsistency^     In  the  latter  case,  the  argument  is  quite  fair,  whatever 
-S^mi,-':::=^^^^^^^^^^^  :-me.u.is  favourable 

same  ma>  ^^^^^^^  ^  ^^  honour  among  thieves,  there  is  no 

ffc  ^  t^e^ -ral  Lul  is  franUly  repudiated.      The  argument  from 


MLLACIES 


311 


authority  is  often  brought  under  this  head:  'such  is  the  opinion  of 
Aristotle.'  Ahhough  this  does  not  establish  the  truth  of  any  proposition, 
it  may  be  fairly  urged  as  a  reason  for  not  hastily  adopting  a  contrary 
conclusion  :  that  is,  of  course,  if  the  subject  under  discussion  be  one  as 
to  which  Aristotle  (or  whoever  the  authority  may  be)  had  materials  for 
forming  a  judgment. 

A  negative  use  of  this  fallacy  is  very  common.  Some  general  doctrine, 
such  as  Positivism,  Transcendentalism,  Utilitarianism,  or  Darwinism,  is 
held  in  common  by  a  group  of  men  ;  who,  however,  all  judge  inde- 
pendently, and  therefore  are  likely  to  differ  in  details.  An  opponent 
exhibits  their  differences  of  opinion,  and  thereupon  pretends  to  have 
refuted  the  theory  they  agree  in  supporting.  This  is  an  argumentum  ad 
scholam,  and  pushes  too  far  the  demand  for  consistency.  But  in  fact  it 
recoils  upon  the  Sophist ;  for  there  is  no  sense  in  quoting  men  against 
one  another,  unless  both  (or  all)  are  acknowledged  to  speak  with  the 
authority  of  learning  and  judgment,  and  therefore  the  general  doctrine 
which  they  hold  in  common  is  the  more  confirmed. 

This,  in  fact,  is  an  example  of  the  paralogism  of  '  proving  too  much  ' ; 
when  a  disputant  is  so  eager  to  refute  an  opponent  as  to  lay  down,  or 
imply,  principles  from  which  an  easy  inference  destroys  his  own  position. 
To  appeal  to  a  principle  of  greater  sweep  than  the  occasion  requires  may 
easily  open  the  way  to  this  pitfall :  as  if  a  man  should  urge  that '  all  men 
are  liars,'  as  the  premise  of  an  argument  designed  to  show  that  another's 
assertion  is  less  credible  than  his  own. 

A  common  form  of  ignoratio  elenchi  is  that  which  Whately  called  the 
'  fallacy  of  objections  ' :  it  consists  in  insisting  upon  all  the  considerations 
against  any  doctrine  or  proposal,  without  any  attempt  to  weigh  them 
against  the  considerations  in  its  favour ;  amongst  which  should  be 
reckoned  all  the  considerations  that  tell  against  the  alternative  doctrines 
or  proposals.  Incontestable  demonstration  can  rarely  be  expected  even 
in  science,  outside  of  the  Mathematics ;  and  in  practical  affairs,  as 
Butler  says,  '  probability  is  the  very  guide  of  life  '  ;  so  that  any  conclusion 
depends  upon  the  balance  of  evidence,  and  to  allow  weight  to  only  a  part 
of  it  is  an  evasion  of  the  right  issue. 

§  8.  Fallacies  in  the  connection  of  premises  and  con- 
clusion that  cannot  be  detected  by  reducing  the  arguments 
to  syllogistic  form,  must  depend  upon  some  juggling  with 
language  to  disguise  their  incoherence.  They  may  be  gener- 
ally described  as  Fallacies  of  Ambiguity,  whether  they  turn 
upon  the  use  of  the  same  word  in  different  senses,  or  upon 
eUipsis. 

Thus  it  may  be  argued  that  all  works  written  in  a  classical  language 
are    classical,    and    that,   therefore,   the    History  of    Philosophy    by 


^i^sm 


mmmamitUB^MKtaM 


312     LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

Diogenes  Laertius.  being  written  in  Greek,  is  a  classic.  Such  ambi- 
guities aie  sometimes  serious  enough;  sometimes  are  httle  better  than 
jokes.  For  jokes,  as  Whately  observes,  are  often  fallacies  ;  and  con- 
sidered as  a  propoedeutic  to  the  art  of  sophistry,  punning  deserves  the 
ignominy  that  has  overtaken  it.  /  \    >    ^-  / 

Fallacies  of  ellipsis  usually  go  by  learned   names,  as ;    (i)  a  auto 
secundum   quid  ad  dictum   simpliciter.      It   has  been  argued   that   smce. 
according  to   Ricardo.   the    value  of  goods  depends   solely  upon    the 
quantity  of  labour  necessary  to  produce  them,  the  labourers  who  are 
employed  upon  (say)  cotton  cloth  ought  to  receive  as  wages  the  whole 
price  derived  from  its  sale,  leaving  nothing  for  interest  upon  capital. 
Ricardo.  however,  explains  that  by  '  the  quantity  of  labour  necessary  to 
produce  goods  '  he  means  not  only  what  is  immediately  applied  to  them 
but  also  the  labour  bestowed  upon  the  implements  and  buildings  with 
which  the  immediate  labour    is   assisted.      Now  these  buildings   and 
implements  are  capital,  the  labour  which  produced  them  was  paid  for 
and  it  was  far  enough  from  Ricardo's  mind  to  suppose  that  the  capital 
which  assists  present  labour  upon  (say)  cotton  cloth  has  no  claim  to 
remuneration  out  of  the  price  of  it.     In  this  argument,  then,  the  word 
labour  in  the  premise  is  used  secundum  quid,  that  is.  with  the  suppressed 
qualification  of  including  past  as  well  as  present  labour  ;   but  in  the 
inference  labour  is  used  simpliciter  to  mean  present  labour  only. 

(2)  A  dicto  secundum  quid  ad  dictum  secundum  altevum  quid.  It  may  be 
urged  that,  since  the  tax  on  tea  is  uniform,  therefore  all  consumers 
contribute  equally  to  the  revenue  for  their  enjoyment  of  it.  tJut 
written  out  fairly  this  argument  runs  thus:  Since  tea  is  taxed  uniformly 
.d  per  lb.,  all  consumers  pay  equally  for  their  enjoyment  of  it  whatever 
quality   they   use.      These    qualifications    introduced,    nobody    can    be 

deceived.  n  j    /  77  ^v, 

U)  A  dicto  simpliciter  ad  dictum  secundum  quid,  also  called  Jallacia 
accidentis.  Thus  :  To  take  interest  upon  aloan  is  perfectly  just  therefore. 
I  do  right  to  exact  it  from  my  own  father  in  distress.  The  popular 
answer  to  this  sort  of  blunder  is  that  '  circumstances  alter  cases.  We 
commit  this  error  in  supposing  that  what  is  true  of  the  average  is  likely 
to  be  true  of  each  case  ;  as  if  one  should  say  :  '  The  offices  are  ready  to 
insure  my  house  against  fire  at  a  rate  per  annum  which  will  leave  them 
heavy  losers  unless  it  lasts  a  hundred  years;  so.  as  we  are  told  not  to 
take  long  views  of  life,  I  shall  not  insure.' 

The  Fallacy  of  Division  and  Composition  consists  in  suggesting,  or 
assuming,  that  what  is  true  of  things  severally  denoted  by  a  term  is  true 
of  them  taken  together.  That  every  man  is  mortal  is  generally 
admitted,  but  we  cannot  infer  that,  therefore,  the  human  race  will 
become  extinct.  That  the  remote  prospects  of  the  race  are  tragic  may 
be  plausibly  argued,  but  not  from  that  premise.  ^  .  .  .  ,.  ..  . 
Chan<^ing  the  Premises  is  a  fallacy  usually  placed  in  this  division . 


FALLACIES 


313 


although,  instead  of  disguising  different  meanings  under  similar  words, 
it  generally  consists  in  using  words  or  phrases  ostensibly  differing,  as  if 
they  were  equivalent :  those  addressed  being  expected  to  renounce  their 
right  to  reduce  the  argument  to  strict  forms  of  proof,  as  needless 
pedantry  in  dealing  with  an  author  so  palpably  straightforward.  If  an 
orator  says — '  Napoleon  conquered  Europe  ;  in  other  words,  he  murdered 
five  millions  of  his  fellow  creatures  ' — and  is  allowed  to  go  on,  he  may 
infer  from  the  latter  of  these  propositions  many  things  which  the  former 
of  them  would  hardly  have  covered.  This  is  a  sort  of  hyperbole,  and 
there  is  a  corresponding  meiosis.  as :  '  Mill  admits  that  the  Syllogism 
is  useful ' ;  when,  in  fact,  that  is  Mill's  contention.  It  may  be  supposed 
that,  if  a  man  is  fool  enough  to  be  imposed  upon  by  such  transparent 
colours,  it  serves  him  right;  but  this  harsh  judgment  will  not  be  urged 
by  any  one  who  knows  and  considers  the  weaker  brethren. 

§  9.  The  above  classification  of  Fallacies  is  a  rearrangement 
of  the  classifications  adopted  by  Whately  and  Mill.  But 
Fallacies  resemble  other  spontaneous  natural  growths  in  not 
submitting  to  precise  and  definite  classification.  The  same 
blunders,  looked  at  from  different  points  of  view,  may  seem  to 
belong  to  different  groups.  Thus,  the  example  given  above  to 
illustrate  fallacia  accidentis,  '  that,  since  it  is  just  to  take 
interest,  it  is  right  to  exact  it  from  one's  ow^n  father,'  may  also 
be  regarded  ^s  petitio  principii,  if  w^e  consider  the  unconditional 
statement  of  the  premise— 'to  take  interest  upon  a  loan  is 
perfectly  just ' ;  for,  surely,  this  is  only  conditionally  true.  Or, 
again,  the  first  example  given  of  simple  ambiguity — *  that 
whatever  is  wTitten  in  a  classical  language  is  classical,  etc.\ 
may,  if  we  attend  merely  to  the  major  premise,  be  [rta'.ed  as  a 
bad  generalisation,  an  undue  extension  of  an  inference,  founded 
upon  a  simple  enumeration  of  the  first  few  Greek  and  Latin 
works  that  one  happened  to  remember. 

It  must  also  be  acknowledged  that  genuine  wild  fallacies, 
roaming  the  jungle  of  controversy,  are  not  so  easily  detected  or 
evaded  as  specimens  seem  to  be  when  exhibited  in  a  Logician's 
collection ;  where  one  surveys  them  without  fear,  like  a  child 
at  a  menagerie.  To  assume  the  succinct  mode  of  statement 
that  is  most  convenient  for  refutation,  is  not  the  natural  habit 
of  these  things.     But  to  give  reality  to  his  account  of  fallacies 


If 


f 


314     LOGIC:    DEDUCTIVE   AND   INDUCTIVE 

an  author  needs  a  large  space,  that  he  may  quote  no  inconsider- 
able part  of  literature  ancient  and  modern. 

As  to  the  means  of  avoiding  fallacies,  a  general  increase  of 
sincerity  and  candour  amongst  mankind  may  be  freely 
recommended.  With  more  honesty  there  would  be  fewer  bad 
arguments  ;  but  there  is  such  a  thing  as  well-meaning  mca- 
pacity  that  gets  unaffectedly  fogged  in  converting  A.,  and 
regards  the  refractoriness  of  O.,  as  more  than  flesh  and  blood 
can  endure.  Mere  indulgence  in  figurative  language,  again,  is 
a  besetting  snare.  "One  of  the  fathers,  in  great  severity, 
calltd  poesy  vimim  dccmonum,''  says  Bacon  :  himself  too  fanciful 
for  a  philosopher.  Surely,  to  use  a  simile  for  the  discovery  of 
truth  is  like  studying  beauty  in  the  bowl  of  a  spoon. 

The  study  of  the  natural  Sciences  trains  and  confirms  the 
mind  in  a  habit  of  good  reasoning,  which  is  the  surest 
preservative  against  i)arulogism,  as  long  as  the  terms  in  use 
are,  like  those  of  science,  well  defined  ;  and  where  they  are  ill 
defined,  so  that  it  is  necessary  to  guard  against  ambiguity,  a 
thorough  training  in  politics  or  metaphysics  may  be  useful. 
Logic  seems  to  me  (I  must  confess)  to  serve,  to  some  extent, 
both  these  purposes.  The  conduct  of  business,  or  experience, 
a  sufficient  time  being  granted,  is  indeed  the  best  teacher,  but 
also  the  most  severe  and  expen-ive.  I  n  the  seventeenth  century 
some  of  the  greatest  philosophers  wrote  de  ititellectiis  emen- 
datione ;  and  if  their  successors  have  given  over  this  very 
practical  inquiry,  the  cause  of  its  abandonment  is  not  success 
and  satiety  but  despair.  Perhaps  the  right  mind  is  not  to  be 
made  by  instruction,  but  can  only  be  bred.  This  is  a  slow 
process,  and  meanwhile  the  rogue  of  a  sophist  may  count  on  a 
steady  supply  of  dupes  to  amuse  the  tedium  of  many  an  age. 


FINIS. 


QUESTIONS 

TU  folloiiing  questions  are  chiefly  taken  from  public  examination  papers  : 
Civil  Service  [S] .  Oxford  [OJ  ,  and  Cambridge  [C] . 

I.  TERMS.  ETC. 

1.  What  is  a  Term?      Explain   and   illustrate  the  chief  divisions  of 

Terms.     What  is  meant  by  the  Connotation  of  a  Term  ?     Illus- 
trate.    [S] 

2.  "  The  connotation  and  denotation  of  terms  vary  inversely."     Ex- 

amine this  assertion,  explaining  carefully  the  limits  within  which 
it  is  true,  if  at  all.     [S] 

3.  Exemplify  the  false  reasoning  arising  from  the  confusion  of  Con- 

trary and  Contradictory  Terms.      [S] 

4.  Discuss   the   claims   of  the   doctrine  of  Terms  to  be  included  in 

a  Logical    System.      Distinguish    between    a    General   and   an 
Abstract  Term.      [S] 

5.  Explain  and  illustrate  what  is  meant  by  the  Denotation  and  Conno- 

tation of  a  Term.     What  terms  have  both,  and  what  have  one 
only  ?      [S] 

6.  Distinguish  between  Abstract  and  Concrete  Names.      To  which  of 

these  classes  belong  (a)  adjectives,   {b)  names  of  states  of  con- 
sciousness ?     Are  any  abstract  names  connotative  ?     [S] 

7.  Distinguish  between  {a)  Proper  and  Singular  Terms,  {b)  Negative 

and  Privative,  {c)  Absolute  and  Relative.     Illustrate. 

8.  What   connection    is    there    between   the    Connotation    and    the 

Relativity  of  Names  ? 

9.  Examine  the  logical  relations  between  the  following  pairs  of  terms : 

{a)  happy  and  happiness  ;  {b)  happy  and  unhappy  ;    {c)  '  the  jury- 
man '  and  '  the  jury  ' ;   (d)  parent  and  offspring. 
Explain  the  technical  words  used  in  your  answer.     [C] 

10.  Distinguish  between  name;  part  of  speech;  term:  and  illustrate  by 

reference  to  the  following— use,  useful,  usefully.      [C] 

11.  Describe  the  nature  of  Collective  terms  ;  examining  in  particular  any 

difticulties  in  distinguishing  between  these  and  general  or  abstract 
terms.     [C] 


3i6     LOGIC:    DEDUCTIVE   AND    INDUCTIVE 

12.  Distinguish  between  positive,  negative,  and  privative  names.  Of  what 
kind  are  the  following,  and  why  —  parallel,  alien,  idle,  un- 
happy ?  What  ambiguity  is  there  in  the  use  of  such  a  term  as 
"not- white"?     [C] 


II.  PROPOSITIONS  AND  IMMEDIATE  INFERENCE 

13.  What  is  meant  by  (i)  the  Conversion,  and  (2)   the  Contraposition 

of  a  proposition  ?  Apply  these  processes,  as  far  as  admissible, 
to  the  following  : — 

{a)  All  invertebrates  have  cold  blood. 

(h)  Some  cold-blooded  animals  are  not  invertebrates. 

(c)  No  wingless  birds  are  songsters. 

{d)  Some  winged  birds  are  not  songsters. 
What  can  you  infer  from  (a)  and  (6)  jointly,  and  what  from  {c)  and 

{d)  jointly  ?      [S] 

14.  "  The  author  actually  supposes  that,  because   Professor  Fawcett 

denies  that  all  wealth  is  money,  he  denies  that  all  money  is 
wealth. "  Analyse  the  differences  of  opinion  implied  in  the  above 
passage.     [S] 

15.  Take     any    universal     affirmative     proposition  ;     convert    it    by 

obversion  (contraposition) ;  attach  the  negative  particle  to  the 
predicate,  and  again  convert.  Interpret  the  result  exactly,  and 
say  whether  it  is  or  is  not  equivalent  to  the  original  proposition. 

[S] 

16.  What   information   about   the  term   "solid  body"  can  we  derive 

from  the  proposition,  "No  bodies  which  are  not  solids  are 
crystals"?     [S] 

17.  Discuss  the  proposal  to  treat  all  propositions  as  affirmative. 

18.  Convert  the  proposition  "A  is  probably  B."     What  information 

does  the  proposition  give  us  concerning  B  ?     [S] 
ig.  Show  in  how  many  ways  you  can  deny  the  following  assertions : 
All  cathedral  towns  are  all  cities ;  Canterbury  is  the  Metropolitan 
see.     [S] 

20.  Explain   the  nature  of  a  hypothetical  (or  conditional)  proposition. 

What  do  you  consider  the  radical  difference  between  it  and  a 
categorical  ?     [S] 

21.  What  is  the  function  of  the  copula  f    In  what  different  manners  has 

it  been  treated  ?     [S] 

22.  Convert   "A  killed   C   unjustly":    "All   Knowledge  is  probably 

useful  "  ;  "  The  exception  proves  the  rule  "  ;  "  Birds  of  a  feather 
flock  together."     [S] 

23.  What  is  modality?     How  are  modals  treated  by  {a)  formal  logic 

and  ip)  by  the  theory  of  induction  ?    [S] 


QUESTIONS  317 

24.  What  is  the  subject  of  an  impersonal  proposition  ?     Give  reasons 

for  your  answer.      [S] 

25.  Is  a   categorical  proposition  sufficiently  described  as  referring  a 

thmg  or  things  to  a  class  ?     [S] 

26.  Enumerate  the  cases  in  which  the  truth  or  falsity  of  one  proposition 

may  be  formally  inferred  from  the  truth  or  falsity  of  another 
Illustrate  these  cases,  and  give  to  each  its  technical  name      [S] 

27.  Illustrate  the  relation  of  Immediate  Inferences   to   the  Laws  of 

Thought. 

28.  Explain   what  is  meant  by  {a)  Symbolic  Logic ;  {h)  the  Logic  of 

Relatives.  Describe  some  method  of  representing  propositions 
by  means  of  diagrams  ;  and  indicate  how  far  any  particular  theory 
of  the  import  of  propositions  is  involved  in  such  representation. 

29.  Explain  the  exact  nature  of  the  relation  between  two  Contradictory 

propositions;   and  define  Conversion  by  Contraposition,   deter- 
mining what  kind  of  propositions  admit  of  such  conversion 
Give   the   contradictory   and    the   contrapositive   of   each  of  the 
following  propositions  :— 
{a)  All  equilateral  triangles  are  equiangular ; 
{b)  No  vertebrate  animal  has  jaws  opening  sideways ; 
(c)  Wherever  A  and  B  are  both  present,  either  C  or  D  is  also 
present.     [S] 

30.  Define  Obversion  and  Inversion,  and  apply  these  processes  also  to 

the  above  three  propositions. 

31.  Propositions  can  be  understood  either  in  extension  or  in  intension 

Explain  this,  and  discuss  the  relative  value  of  the  two  interore 
tations.     [S]  ^ 

32.  Distinguish  between  real  and  verbal  propositions;  and  explain  the 

importance  of  the  distinction. 
ZZ-  Illustrate  the  process  called  '  change  of  Relation.' 


III.  SYLLOGISM  AND  MEDIATE  INFERENCE 

34  What  is  a  Syllogism  ?  Find,  without  reference  to  the  mnemonic 
verses,  in  what  different  ways  it  is  possible  to  prove  syllogistically 
the  conclusion  No  S  is  P;  and  show  the  equivalence  between 
these  different  ways.      [S] 

35.  From  what  points  of  view  can  the  syllogism  be  regarded  (i)  as 
being,  (2)  as  not  being,  a  petitio  principii  ?     [S] 

Ze.  What  are  the  figures  of  syllogism  ?  For  what  kind  of  arguments  are 
they  severally  a  dapted  ?     [S] 

Z7-  What  is  meant  by  Mood  and  Figure?  How  can  the  validity  of 
a  Mood  be  tested  ?    Should  there  be  four  Figures  or  three  ?    [S] 


3i8     LOGIC:   DEDUCTIVE   AND   INDUCTIVE 

38.  Construct  syllogisms  in  Camenes,  Datisi  and  Baroco,  and  reduce 
them  to  the  corresponding  moods  of  the  first  figure. 

3Q.  Explain  the  meaning  of  "  ostensive "  and  "indirect"  Reduction. 
Show   that   any   Mood  of  the  second    Figure  may  be  reduced 

in  either  way. 

40.  Show  that  A.  cannot  be  proved  except  in  the  First  Figure.     Express 

the  following  reasoning  in  as  many  syllogistic  figures  as  you  can : 
Some  theorists  cannot  be  trusted,  for  they  are  unwise.     [S] 

41.  Discuss  the  possibility  of  reducing  the  argument  a  fortiori  to  the 

syllogistic  form.      [S] 

42.  Can  a  false  conclusion  be  reached  through  true  premises,  or  a  true 

conclusion    through    false    premises?      Give    reason    for    your 

answer.      [S] 

43.  Can  we  under  any  circumstances  infer  a  relation  between  X  and  Z 

from  the  premises— Some  Y's  are  X's 

Some  Y's  are  Z's?     [S] 

44.  fake  an  apparent  syllogism  subject  to  the  fallacy  of  negative  pre- 

mises, and   inquire  whether  you  can  correct  the  reasoning  by 
converting  one  or  both   of  the  premises  into  the  affirmative 

form.      [S] 

45.  Enumerate  the  faults  to  which  a  syllogism  is  liable,  giving  instances 

of  each.     [S] 
46._State  any  Enthymeme,  and  expand  it  into  (i)  a  Syllogism,  (2)  an 
NEpicheirem^tJTa  Sorites;  and  give  in  each  case  the  technical 
mime^the  Mood  or  Order  that  results. 

47.  Stat^y^y  Disjunctive. -Syllogism,  and  change  it  (i)  into  a  Hypo- 

thfetical,  (2)  into  a  Categorical ;    and  discuss  the  loss  or  gain, 
in  cogency  or  significance,  involved  in  this  process. 

48.  Can    the   Syllogism   be   treated   as   merely  a  consequence  of  the 

"  Laws  of  Thought  "  ?     If  not,  why   not  ;  and  what  else  does  it 

imply  ? 

49.  Prove  that  with  three  given  propositions  (of  the  forms  A.,  E..  I.,  O.) 

it  is  never  possible  to  construct  more  than  one  valid  syllogism. 

50.  Distinguish  between  a  Constructive  and  a  Destructive  Hypothetical 

Syllogism ;    and  show  how  one  may  be  reduced  to   the  other. 
[C] 


IV.  INDUCTION,  ETC.  ^1 

51.  What  constitutes  a  Valid  Induction  ?     Distinguish  it  from  a  legiti- 

mate hypothesis.     [S] 

52.  Is  it  possible  to  form  true   universal   propositions  about  facts  if 

we  have  not  actually  observed  all  the  individuals  designated  by 
the  subject  of  the  proposition  ?     If  so,  how  ?     [S] 


QUESTIONS 


3»9 


53  "Perfect  induction  is  demonstrative  and  •  syllogistic ;  imperfect 
induction  is  neither."  Explain  the  difference  between  perfect 
and  imperfect  induction,  and  examine  the  truth  of  this  asser- 
tion.     [S] 

54.  Why  is  it  that  one   should  not   regard   night   as   the   cause,   nor 

even   as   a   universal  condition  of  day  ?     Explain  "cause"  and 
condition.      [S] 

55.  What  do  you  understand  by  an  experiment  ?     Can  you  say  how 

many  experiments  are  required  to  establish  (i)  a  fact,  (2)  a  law  of 
nature  ? 

56.  How  would  you  define  antecedent,  cause,  effect,  consequent  ?     [S] 

57-  England  is  the  richest  country  in  the  world,  and  has  a  gold 
currency.  Russia  and  India,  in  proportion  to  population, 
are  poor  countries  and  have  little  or  no  gold  currency.  How  far 
are  such  kind  of  facts  logically  sufficient  to  prove  that  a  gold 
currency  is  the  cause  of  a  nation's  wealth  ?      [S] 

58.  A  man  having  been  shot  through  the  heart  immediately  falls  dead 
Investigate  the  logical  value  of  such  a  fact  as  proving  that  all  men 
shot  through  the  heart  will  fall  dead.     [S] 

59  Explain  the  process  of  induction  called  the  Method  of  Difference, 
and  give  some  new  instances  of  its  application.  How  is  it  related 
to  the  Method  of  Concomitant  Variations  ?  What  is  the  Major 
Premise  implied  in  all  these  methods  ?     [S] 

60.  Explain  the  logical  cogency  of  experiments  in  the  search  for  physical 

causes.     [S] 

61 .  If  the  effects  of  A  B  C  D  are  fully  expressed  by  a  b  c  d .  and  those  of  B      / 

C  D  by  b  c  d,  what  inductive  inference  can  be  drawn  and  on  what-  y 
principle  ?     State  the  canon  according  to  which  it  is  drawn.     [S]  ^^" 

62.  Compare  the  advantage  of  observation  and  experiment  as  means  of 

gaining  data  for  Reasoning.     [S] 

63.  Compare  the  cogency  of  different  Inductive  Methods,  showing  the 

kind  of  evidence  each  requires,  and  the  principle  on  which  it  is 
based.     [S] 

64.  Compare  the  Canons  of  Agreement  and  Difference  (i)  as  to  the 

difficulty  of  fitting  them  with  actual  "  Instances, "  and  (2)  as  to 
their  conclusiveness. 

65.  Describe  what  is  meant  by  residual  phenomena,  and  estimate  their 

value  in  inductive  science.     [SJ 

66.  What  is  the  argument  from  Analogy  ?     How  does  it  differ  from  (a) 

Induction,  {b)  Metaphorical  argument  ?     [S] 

67.  What  are  the  various  senses  in  which  the  word  Analogy  has  been 

used  ?     Distinguish,   giving  instances,  between  good  and   bad 
analogies.     [S] 

68.  How  do  you  distinguish  between  what  Mill  calls  the  Geometrical, 

Physical  and  Historical  Methods  ? 


320      LOGIC:    DEDUCTIVE   AND    INDUCTIVE 


69 


70. 


71- 


72. 

73 

74- 
75- 


What  is  meant  by  a  doctrine  being  unverifiable  ?  If  a  conclusion 
reached  by  deduction  does  not  agree  with  the  facts,  where  must 
we  look  for  error  ? 

There  are  certain  cases  in  which  failure  of  verification  is  fatal  to  a 
theory  and  other  cases  in  which  it  is  of  comparatively  little 
cogency.  How  would  you  distinguish  between  these  classes  of 
cases  ?      [S] 

Taking  the  "evolution,"  or  any  other  proposed  hypothesis,  how 
should  one  proceed  {a)  to  show  whether  it  satisfies  the  conditions 
of  a  legitimate  hypothesis  sufficiently  to  entitle  it  to  investigation, 
and  (b)  to  test  it  with  a  view  to  its  acceptance  or  rejection  as  a 
truth  of  science  ?      [S] 

What  do  you  mean  by  saying  that  "a  phenomenon  has  been 
satisfactorily  explained  "  ? 

Explain  and  illustrate  the  Historical  Method  of  Sociological 
inquiry.      [S] 

What  is  the  relation  of  the  theory  of  Probability  to  Logic  ?      [S] 

Explain  and  discuss  the  doctrine  that  Induction  is  based  upon  the 
Theory  of  Probability.      [S] 

76.  Explain  the  nature  and  use  of  Classification,  the  means  to,  and  tests 

of,  its  successful  performance.      [S] 

77.  What  is  Definition  and  what  is  its  use  ?     Mention  various  difficulties 

that  occur  in  the  process,  and  show  how  they  are  to  be  met.      [S] 
78    Propose  rules   for   a  good    Division   and   a  good    Definition   and 
exemplify  the  breach  of  them.      [S] 

79.  Examine  the  validity  of  the  idea  of  Real  Kinds.      [O] 

80.  What  kind  of  words  are  indefinable,  and  why  ?     When  do  we  define 

by  negation  and  by  example  ?      [S] 

81.  Distinguish  between  the  province  and  aims  of   classification  and 

(logical)  division.     Illustrate.      [S] 

82.  What  is  an  infima  species  or  species  specialissima?     Compare  the  use 

of  the  terms  genus  and  species  in  Logic  with  that  which  is  common 
in  speaking  of  animals  or  plants.      [S] 

83.  How  far   does   the  formation    of    Definitions   and    Classifications 

constitute  the  end  of  Science  ?      [S] 

84.  Examine  the  methodological  relations  between  Definition,  Classifi- 

cation and  Nomenclature.      [S] 

85.  Give  instances  of  "  Differentia,"    "Property,"    "Inseparable    Acci- 

dent "  ;  and  examine,  with  reference  to  your  instances,  how  far  it 
is  possible  to  distinguish  them.     [S] 


QUESTIONS 


V.  MISCELLANEOUS. 


321 


88 


89. 


100. 


"  People  can  reason  without  the  help  of  Logic."  Why  is  this  not  a 
sufficient  objection  to  the  study?  In  your  answer  show  dis- 
tinctly why  Logic  should  be  studied.      [S] 

What  is  the  meaning  of  the  assertion  that  Logic  is  concerned  with 
the  form,  and  not  with  the  matter,  of  thought  ?      [S] 

"  Neither  by  deductive  nor  inductive  reasoning  can  we  add  a  tittle 
to  our  implicit  knowledge."    (Jevons.)    Explain  and  criticise.    [S] 

What  is  the  logical  foundation  of  the  indirect  method  or  rediictio  ad 
ahsurdiun  ?    Is  it  applicable  to  non-mathematical  subjects  ?     [S] 

On  what  grounds  do  we  believe  in  the  reality  of  a  historical  event  ? 
[SJ    • 

"  Facts  are  familiar  theories."     Explain  and  discuss  this.     [O] 

Wherein  lies  the  difficulty  of  proving  a  negative  ?     [OJ 

Can  any  limits  be  assigned  to  the  possible  unification  of  the  sciences  '> 

Are  the  results  of  inductive  inference  necessarily  certain  ?     [O]     -  /  *^' 
The   method   of  deductive   science  is   hypothetical.     Explain   and 

discuss.      [O]      I  7,^1^^  ^  ^H^\ 
"The  uniformity  of  Nature  can  never   be  more   than   a  working 

hypothesis. ' '     Explain  and  criticise. 
"Without  speculation  there  is  no  good  and  original  observation  " 

Why  ?      [O] 

Can  the  provinces  of  induction  and  deduction  be  kept  separate  ? 

How  far  is  the  relation  of  logical  dependence  identical  with  that  of 
causation  ?      [O] 

State  in   syllogistic   form   (mood   and   figure)  the  following  argu- 
ments : — 

[a)  As  polygamy  is  in  many  countries  legal,  we  may  infer  the 
variability  of  the  moral  standard. 

{b)  If  gold  is  wealth,  to  export  it  diminishes  the  national 
resources. 

{c)  If  all  good  people  are  happy,  unhappiness  is  an  indication 
of  vice. 

{d)  One  may  be  sure  of  the  benefits  of  inuring  young  children 
to  cold,  from  the  strength  exhibited  by  all  men  and  women  thus 
treated  in  infancy. 

{e)  Where  there  is  no  law,  there  is  no  injustice. 

(/)  "  Dissimulation  is  but  a  faint  kind  of  policy  or  wisdom  ; 
for  it  asketh  a  strong  wit  and  a  strong  heart  to  know  when  to 
tell  the  truth,  and  to  do  it ;  therefore  it  is  the  weaker  sort  of 
politicians  that  are  the  greatest  dissemblers."     (Bacon.) 

{g)  Money  being  a  barren  product,  it  is  contrary  to  nature  to 

X 


OLA^ 


Cw- 


322      LOGIC  :  DEDUCTIVE   AND   INDUCTIVE 

make  it  reproduce  itself.     Usury,  therefore,  is  unnatural,  and, 
being  unnatural,  is  unjustifiable. 

(h)  The  study  of  mathematics  is  essential  to  a  complete 
course  of  education,  because  it  induces  a  habit  of  close  and 
regular  reasoning.  [S] 
y^Toi.  Explain  and  illustrate  the  following  terms  :—Subalternans,  Vera 
Causa,  Plurality  of  Causes,  Law  of  Nature,  Empirical  Law, 
Summiim  Genus,  Predicament,  A  rbor  Porphyriana,  Axiom,  Universe 
of  discourse  {suppositio),  Antinomy,  Dilemma,  Realism,  Dichotomy. 
~lo2.  Is  there  any  distinction  and,  if  so,  what,  between  a  complete 
Description  and  an  Explanation  ?     [C] 

103.  On  what  principles  have  Fallacies  been  classified  ?     To  what  extent 

do  you  think  a  satisfactory  classification  of  Fallacies  possible  ? 
[C] 

104.  Examine  how  far  conceptions  of  Persistence  and  of  Invariable 

Concomitance  of  Properties  are  involved  in  the  methodolo- 
gical application  of  the  conception  of  Cause. 
Inquire  whether  the  two  following  propositions  can  be  reconciled 
with  one  another :  (a)  The  same  conjunction  of  antecedents  is 
invariably  followed  by  the  same  consequent ;  {h)  We  never  find 
the  same  concurrence  of  phenomena  a  second  time.      [C] 

105.  Using  the  term  Logic  in  a  wide  sense  so  as  to  include  Methodology, 

inquire  how  far  a  Logic  of  Observation  is  possible,  and  show  in 
what  it  will  consist.      [C] 

106.  What  is  Proof  ?  '  -^^ 
Explain  and  cjiscuss  the  following  dicta: — (a)  Qui  nimium prohdt, 

nihil  prohat :  {h)  A  bad  proof  is  worse  than  no  proof;  (c)  The 
exception  proves  the  rule;  {d)  Negatives  cannot  be  proved.  [C] 
Examine  how  far  the  rules  of  immediate  and  syllogistic  inference 
are  modified  by  differences  of  interpretation  of  the  categorical 
proposition  in  respect  to  the  existence  of  the  subject.  [S] 
"  An  effect  is  but  the  sum  of  all  the  partial  causes,  the  concurrence 

of  which  constitutes  its  existence." 
"  The  cause  of  an  event  is  its  invariable  and  unconditional  ante- 
cedent."    Explain  and  compare  these  two  theories  of  causation. 
Does  either  alone  exhaust  the  scientific  conception  of  cause  ?  [S] 
Under  what  logical  conditions  are  statistical  inferences  authorised, 
and  what  is  the  nature  of  their  conclusions  ?      [S] 
no.  Distinguish  between  Psychology,   Metaphysics,   and  Logic;   and 

discuss  briefly  their  mutual  relations.      [S] 
III.  All  processes  of  inference  in  which  the  ultimate  premises  are  parti- 
cular cases  are  equally  induction. 
Induction  is  an  inverse  deduction. 

Explain  and  contrast  these  two  theories  of  the  relation  of  induc- 
tion to  deduction.     [S] 


109. 


^ 


> 


QUESTIONS  323 

112.  What  are  the  Fallacies  specially  incident    to  Induction  ?-or  to 
the  application  of  the  theory  of  Probabilities  ?     [S] 
What  is  meant  by  the  personal  error  (or  persojial  equation)  in  observa- 
tion ?     Discuss  its  importance  in  different  branches  of  know- 
ledge.     [S] 

Define  and  illustrate  .—Paralogism,  ignoratio  elenchi,  faUacia  acci- 
dentis.  argumentum  ad  verecundiam,  illicit  process,  undistributed 
middle. 


113 


14. 


Printed  by  Ballantyne  Hanson  ^^  Co. 
London  ^  Edinburgh. 


By  GRANT  ALLEN. 
Demy  8vo,  cloth,  20s.  net, 

THE  EVOLUTION  OF  THE  IDEA 

OF  GOD: 

AN  ENQUIRY  INTO  THE  ORIGINS  OF  RELIGIONS. 


SOME  PRESS  OPINIONS. 

AZt'irf.t^{  fv'''V''^'-T''^^^  sympathetic  spirit  in  which  Mr. 
Allen  treats  a  delicate  and  complex  subject  should  have  kindly  con- 

nhonftr       ""  ^^""V  '•'^°"'  ^'^^  '^""'y  °f  "^'^"'s  beliefs  and  guesses 

nf^^Vf  iTTi^^'^^'^PP^^^ A  book  which  is  the  oStcome 

of  careful  scholarly  research." 

c.n^tJ^'"''^'^''^™^-  ^°°^'  *^^  outcome  of  twenty  years  of  thought 
trihnHnnrrth^'l"'"'^'  IS  Certainly  one  of  the  most  important  con- 

r  s  Pi?^^^^  ^  ^'\\7V^  '^'^  ^^""^^"  "^^"d  ^^'i^h  the  last  decade 
nas  given  us.  .  .  .  We  have  no  space  to  trace  further  the  unfcldin? 
of  these  suggestive  Ideas,  which  are  developed  and  illustrated  with 

work^  mT  An^''''""'^"  "I  ^'°^^  °^  ^^•■'°"^  P^'-P^^^^-  The  present 
uork  Mr  Allen  says,  is  but  a  sketch  which  wdl  be  fil'ed  m  and 
amplified  if  the  public  is  sufficiently  interested  - 

suc^essfulT Mr '?!?."  °^  '^^  "^°''  ambitious  and  net  the  least 
successful  of  Mr.  Aliens  works.  ...  It  is  needless  to  say  that  the 
book  IS  clever,  showing  marks  of  wide  reading,  ingenuity,  and  a 

rPnl^n  r^'f^''"""''^-^^'  '^^  ^''^^^'  ^^^  ^^at  it  altracts  by^tl  e  very 
reason  that  the  writer  is  cumbered  with  few  doubts  or  misgivings  as 
o  he  soundness  of  his  theories The  true  student  of  the  sub- 
ject will  profit  much  by  Mr.  Grant  Allen's  erudition  and  his  cri.icisnis 
of  the  work  of  his  predecessors."  '^i^mb 

int^rL^*  5*  ^^''^L«'"theZ)«//j.lAz//._"  A  work  of  extraordinary 
interest  and  sugges  ion.  ...  It  is  on  the  whole  a  worthy  treatmem 
Sinf  i™"!f"'''^^  interesting  subject,   a  book  for  the   intelligen 
general  reader,  one  of  the  books  that  bristle  with  thealvvavsplau  fble 
and  frequently  convincing,  reason  why."  "    ^  ^"^'"^'" 

T^e  Scotsman.—"  It  will  be  understood  by  every  one  thit  thp 
subject  Mr.  Allen  has  chosen  would  be  handle7by  him  n  a 
thoroughly  scientific  manner,  and  in  absolute  independence  of  aU 
Geological  theories.  ...  The  writer  has  collected  an  immense 
tT.^  f  °^I^'''  ^'-'^""^  ^'^  '^^  development  of  religion,  andTi^s  pm 
o  tt  wfn  1''  "'  ""  "^of  interesting  way.  I  he  mSre  educated  par 
of  the  world  is  prepared  for  a  work  like  this,  and  we  have  no  doub 
it  will  be  read  by  many  with  the  deepest  interest." 


GRANT   RICHARDS, 

9  HENRIETTA   STREET,   COVENT  GARDEN,   W.C. 


I 


By  EDWARD  CLODD. 

Second  Edition.     Crown  8vo,  cloth,  5s.  net. 

PIONEERS   OF   EVOLUTION 

FROM 

THALES  TO  HUXLEY. 

WITH  AN   INTERMEDIATE  CHAPTER  ON  THE 
CAUSES  OF  ARREST  OF  THE  MOVEMENT. 

With  Photogravure  Portraits  of  Charles  Darwin,  Prof.  Huxley. 
Mr.  A.  R.  Wallace,  and  Mr.  Herbert  Spencer. 


SOME  PRESS  OPINIONS. 

The  Times.—''  We  are  always  glad  to  meet  Mr.  Edward  Clodd. 
He  is  never  dull ;  he  is  always  well  informed,  and  he  says  what  he 
has  toTay  whh  clearness  and  incision.  .  .  .  The  interest  intensifies  as 
Mr  Clodd  attempts  to  show  the  part  really  played  in  the  growth  of 
he  doctrine  of  evolution  by  men  like  Wallace.  Darwin,  Huxley,  and 
Soencer.  Mr.  Clodd  clears  away  prevalent  misconceptions  as  to 
^h?  work  of  hese  modern  pioneer^.  Especially  does  he  give  to 
Mr.  S^ncer  the  credit  which  is  his  due.  but  which  ^^^  often  mistakenly 
award^  to  Darwin.  Mr.  Clodd  does  not  seek  m  the  least  to  lov^er 
Darwin  from  the  lofty  pedestal  which  he  rightly  occupies  ;  he  only 
seeks  to  show  precisely  why  he  deserves  to  occupy  such  a  position. 
We  comn.end?he  book  to  those  who  want  to  know  what  evoUuron 
really  means ;  but  they  should  be  warned  beforehand  that  they 
have  to  tackle  strong  meat." 

The  Daily  Chronicle.-'' The  goal  to  which  Mr  Clodd  leads  us 
in  so  masterly  a  fashion  in  the  present  volume  is  but  the  starting- 
point  o"f  esh'achievements.  and,  in  due  course,  fresh  theones^  His 
book  furnishes  an  important  contribution  to  a  liberal  education. 

Scotsman.—"  There  is  no  better  book  on  the  subject  for  a  general 
reader,  and  while  its  matter  is  largely  familiar  to  professed  students 
of  sdence,  and  indeed  to  most  men  who  are  well  read,  no  one  could 
go  through  the  book  without  being  both  refreshed  and  nevvly 
fnstructed  by  its  masterly  survey  of  the  growth  of  the  most  powerful 
idea  of  modern  times."       

GRANT   RICHARDS, 

9  HENRIETTA   STREET,   COVENT  GARDEN,   W.C. 


By  LOUIS  WALDSTEIN,  M.D. 
Fcap.  8vo,  cloth,  3s.  6d. 

THE    SUBCONSCIOUS    SELF 

AND 

ITS  RELATION  TO  EDUCATION 
AND  HEALTH. 

SOME  PRESS  OPINIONS. 

The  Daily  Mail.—"  The  thoughtful  inquirer  into  psychology 
will  find  much  to  engage  his  attention  in  Dr.  Louis  Waldstein's 
treatise." 

The  Sun.— "For  thoughtful  readers,  and  for  that  constantly 
growing  yet  unostentatious  class  of  people  to  whom  culture  comes 
only  as  the  result  of  many  moments  snatched  from  the  struggling 
round  of  life,  Dr.  Waldstein's  studies  will  be  something  of  an 
intellectual  tonic  as  well  as  a  mental  search-light." 

The  Manchester  Guardiati. — '  'An  interesting  and  suggestive  essay 
in  which  the  author,  steering  his  way  fairly  clear  between  the 
requirements  of  a  work  addressed  to  the  public  and  the  more 
technical  details  of  medical  psychology,  urges  with  some  force  that 
'  certain  peculiarities  and  failings '  of  our  nervous  organisation  '  may 
be  accounted  for  by  causes  more  readily  understood  than  by  the 
assumption  of  hereditary  influences,'  namely,  by  the  early  experi- 
ences which  pass  unnoticed,  though  not  unregistered,  by  the  mind, 
and  may  therefore  be  designated  by  the  term  '  subconscious.'  " 

Sheffield  Indepe?ident.—"^e  leave  Mr.  Waldstein's  treatise, 
which  is  written  throughout  with  lucidity  and  directness,  to  those 
whose  interests,  from  medical  or  merely  human  reasons,  have  led 
them  to  study  the  strange  and  startling  movements  of  psychological 
phenomena.  They  will  find  much  to  interest ;  much,  no  doubt,  to 
challenge,  and  something  to  be  learnt  from  the  author's  attempt  to 
adjust  the  balance  between  the  workings  of  that  subconscious  self  he 
has  defined  as  the  result  of  impressions  on  our  senses  in  plastic 
moments,  and  the  manifestations  of  our  conscious  menial  powers,  in 
their  struggle  for  dominance  in  our  dual  nature." 


GRANT   RICHARDS, 

9  HENRIETTA  STREET,   COVENT  GARDEN,   W.C. 


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Appendix  by  Lord  Charles  Beresfokd.  With  Map, 
glob3  Svo,  buckram,  3s.  6d. 


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